diff --git a/ion/src/shared/events.cpp b/ion/src/shared/events.cpp
index 51cbb733d..0ce13fbdd 100644
--- a/ion/src/shared/events.cpp
+++ b/ion/src/shared/events.cpp
@@ -30,7 +30,7 @@ static constexpr EventData s_dataForEvent[] = {
   TL(), TL(), U(),   U(),  U(),  U(),
   TL(), TL(), TL(), TL(), TL(), TL(),
   T("exp()"), T("ln()"),  T("log()"), T("i"), T(","),      T("^"),
-  T("sin()"), T("cos()"), T("tan()"), T("p"), T("sqrt()"), T("^2"),
+  T("sin()"), T("cos()"), T("tan()"), T("Pi"), T("v()"), T("^2"),
   T("7"), T("8"), T("9"), T("("), T(")"), U(),
   T("4"), T("5"), T("6"), T("*"), T("/"), U(),
   T("1"), T("2"), T("3"), T("+"), T("-"), U(),
diff --git a/poincare/Makefile b/poincare/Makefile
index 759e538ad..25aa347aa 100644
--- a/poincare/Makefile
+++ b/poincare/Makefile
@@ -24,6 +24,7 @@ objs += $(addprefix poincare/src/,\
   matrix.o\
   matrix_data.o\
   multiplication.o\
+  naperian_logarithm.o\
   n_context.o\
   nth_root.o\
   opposite.o\
@@ -31,6 +32,7 @@ objs += $(addprefix poincare/src/,\
   power.o\
   product.o\
   sine.o\
+  square_root.o\
   subtraction.o\
   sum.o\
   symbol.o\
diff --git a/poincare/include/poincare.h b/poincare/include/poincare.h
index 5ee726d56..39eaa3586 100644
--- a/poincare/include/poincare.h
+++ b/poincare/include/poincare.h
@@ -19,6 +19,7 @@
 #include <poincare/matrix.h>
 #include <poincare/matrix_data.h>
 #include <poincare/multiplication.h>
+#include <poincare/naperian_logarithm.h>
 #include <poincare/n_context.h>
 #include <poincare/nth_root.h>
 #include <poincare/opposite.h>
@@ -26,6 +27,7 @@
 #include <poincare/power.h>
 #include <poincare/product.h>
 #include <poincare/sine.h>
+#include <poincare/square_root.h>
 #include <poincare/subtraction.h>
 #include <poincare/sum.h>
 #include <poincare/symbol.h>
diff --git a/poincare/include/poincare/expression.h b/poincare/include/poincare/expression.h
index 190400e78..3d18919d9 100644
--- a/poincare/include/poincare/expression.h
+++ b/poincare/include/poincare/expression.h
@@ -20,6 +20,7 @@ class Expression {
       Logarithm,
       Matrix,
       Multiplication,
+      NaperianLogarithm,
       NthRoot,
       Opposite,
       Fraction,
@@ -27,6 +28,7 @@ class Expression {
       Power,
       Product,
       Sine,
+      SquareRoot,
       Sum,
       Subtraction,
       Symbol,
diff --git a/poincare/include/poincare/global_context.h b/poincare/include/poincare/global_context.h
index c4285216b..43bb17950 100644
--- a/poincare/include/poincare/global_context.h
+++ b/poincare/include/poincare/global_context.h
@@ -20,6 +20,7 @@ public:
 private:
   int symbolIndex(const Symbol * symbol) const;
   Expression * m_expressions[k_maxNumberOfScalarExpressions];
+  Float m_pi;
 };
 
 #endif
diff --git a/poincare/include/poincare/naperian_logarithm.h b/poincare/include/poincare/naperian_logarithm.h
new file mode 100644
index 000000000..34bb9bef2
--- /dev/null
+++ b/poincare/include/poincare/naperian_logarithm.h
@@ -0,0 +1,15 @@
+#ifndef POINCARE_NAPERIAN_LOGARITHM_H
+#define POINCARE_NAPERIAN_LOGARITHM_H
+
+#include <poincare/function.h>
+
+class NaperianLogarithm : public Function {
+public:
+  NaperianLogarithm();
+  float approximate(Context & context) const override;
+  Type type() const override;
+  Expression * cloneWithDifferentOperands(Expression ** newOperands,
+      int numberOfOperands, bool cloneOperands = true) const override;
+};
+
+#endif
diff --git a/poincare/include/poincare/square_root.h b/poincare/include/poincare/square_root.h
new file mode 100644
index 000000000..766d7d753
--- /dev/null
+++ b/poincare/include/poincare/square_root.h
@@ -0,0 +1,16 @@
+#ifndef POINCARE_SQUARE_ROOT_H
+#define POINCARE_SQUARE_ROOT_H
+
+#include <poincare/function.h>
+
+class SquareRoot : public Function {
+public:
+  SquareRoot();
+  float approximate(Context & context) const override;
+  Type type() const override;
+  Expression * cloneWithDifferentOperands(Expression ** newOperands,
+    int numberOfOperands, bool cloneOperands = true) const override;
+  ExpressionLayout * createLayout() const override;
+};
+
+#endif
diff --git a/poincare/include/poincare/symbol.h b/poincare/include/poincare/symbol.h
index 6b80bfdd3..694397b09 100644
--- a/poincare/include/poincare/symbol.h
+++ b/poincare/include/poincare/symbol.h
@@ -6,7 +6,8 @@
 class Symbol : public LeafExpression {
 public:
     enum SpecialSymbols : char {
-        Ans = '^'
+        Ans = '^',
+        Pi = '*'
     };
     Symbol(char name);
     ExpressionLayout * createLayout() const override;
diff --git a/poincare/src/expression_lexer.l b/poincare/src/expression_lexer.l
index 2586d2132..90b1a9838 100644
--- a/poincare/src/expression_lexer.l
+++ b/poincare/src/expression_lexer.l
@@ -81,16 +81,19 @@ E  { return EE; }
 [A-Zxnt] { poincare_expression_yylval.character = yytext[0]; return SYMBOL; }
 abs { poincare_expression_yylval.expression = new AbsoluteValue(); return FUNCTION; }
 diff { poincare_expression_yylval.expression = new Derivative(); return FUNCTION; }
-ans { poincare_expression_yylval.character = Symbol::Ans; return SYMBOL; }
+ans { poincare_expression_yylval.character = Symbol::SpecialSymbols::Ans; return SYMBOL; }
 exp { poincare_expression_yylval.expression = new Exponential(); return FUNCTION; }
 sin { poincare_expression_yylval.expression = new Sine(); return FUNCTION; }
 cos { poincare_expression_yylval.expression = new Cosine(); return FUNCTION; }
 int { poincare_expression_yylval.expression = new Integral(); return FUNCTION; }
 tan { poincare_expression_yylval.expression = new Tangent(); return FUNCTION; }
 log { poincare_expression_yylval.expression = new Logarithm(); return FUNCTION; }
+ln { poincare_expression_yylval.expression = new NaperianLogarithm(); return FUNCTION; }
 root { poincare_expression_yylval.expression = new NthRoot(); return FUNCTION; }
 sum { poincare_expression_yylval.expression = new Sum(); return FUNCTION; }
 product { poincare_expression_yylval.expression = new Product(); return FUNCTION; }
+Pi { poincare_expression_yylval.character = Symbol::SpecialSymbols::Pi; return SYMBOL; }
+v { poincare_expression_yylval.expression = new SquareRoot(); return FUNCTION; }
 \+ { return PLUS; }
 \- { return MINUS; }
 \* { return MULTIPLY; }
diff --git a/poincare/src/global_context.cpp b/poincare/src/global_context.cpp
index 0eefdcac7..baee54faf 100644
--- a/poincare/src/global_context.cpp
+++ b/poincare/src/global_context.cpp
@@ -1,7 +1,9 @@
 #include <poincare/global_context.h>
 #include <assert.h>
+#include <math.h>
 
-GlobalContext::GlobalContext()
+GlobalContext::GlobalContext() :
+  m_pi(Float(M_PI))
 {
   for (int i = 0; i < k_maxNumberOfScalarExpressions; i++) {
     m_expressions[i] = nullptr;
@@ -19,6 +21,9 @@ int GlobalContext::symbolIndex(const Symbol * symbol) const {
 }
 
 const Expression * GlobalContext::expressionForSymbol(const Symbol * symbol) {
+  if (symbol->name() == Symbol::SpecialSymbols::Pi) {
+    return &m_pi;
+  }
   int index = symbolIndex(symbol);
   if (index < 0 || index >= k_maxNumberOfScalarExpressions) {
     return nullptr;
diff --git a/poincare/src/layout/nth_root_layout.cpp b/poincare/src/layout/nth_root_layout.cpp
index 4e0664763..a178ca196 100644
--- a/poincare/src/layout/nth_root_layout.cpp
+++ b/poincare/src/layout/nth_root_layout.cpp
@@ -19,25 +19,31 @@ NthRootLayout::NthRootLayout(ExpressionLayout * radicandLayout, ExpressionLayout
   m_indexLayout(indexLayout)
 {
   m_radicandLayout->setParent(this);
-  m_indexLayout->setParent(this);
-  m_baseline = max(m_radicandLayout->baseline() + k_radixLineThickness + k_heightMargin,
-                   m_indexLayout->size().height() + k_indexHeight);
+  if (m_indexLayout != nullptr) {
+    m_indexLayout->setParent(this);
+    m_baseline = max(m_radicandLayout->baseline() + k_radixLineThickness + k_heightMargin,
+      m_indexLayout->size().height() + k_indexHeight);
+  } else {
+    m_baseline = m_radicandLayout->baseline() + k_radixLineThickness + k_heightMargin;
+  }
 }
 
 NthRootLayout::~NthRootLayout() {
   delete m_radicandLayout;
-  delete m_indexLayout;
+  if (m_indexLayout != nullptr) {
+    delete m_indexLayout;
+  }
 }
 
 void NthRootLayout::render(KDContext * ctx, KDPoint p, KDColor expressionColor, KDColor backgroundColor) {
   KDSize radicandSize = m_radicandLayout->size();
-  KDSize indexSize = m_indexLayout->size();
+  KDSize indexSize = m_indexLayout != nullptr ? m_indexLayout->size() : KDSize(k_leftRadixWidth,0);
   KDColor workingBuffer[k_leftRadixWidth*k_leftRadixHeight];
   KDRect leftRadixFrame(p.x() + indexSize.width() + k_widthMargin - k_leftRadixWidth,
     p.y() + m_baseline + radicandSize.height() - m_radicandLayout->baseline() + k_heightMargin - k_leftRadixHeight,
     k_leftRadixWidth, k_leftRadixHeight);
   ctx->blendRectWithMask(leftRadixFrame, expressionColor, (const uint8_t *)radixPixel, (KDColor *)workingBuffer);
-  if (m_indexLayout->size().height() + k_indexHeight > m_radicandLayout->baseline() + k_radixLineThickness + k_heightMargin) {
+  if (indexSize.height() + k_indexHeight > m_radicandLayout->baseline() + k_radixLineThickness + k_heightMargin) {
     ctx->fillRect(KDRect(p.x() + indexSize.width() + k_widthMargin,
                          p.y() + indexSize.height() + k_indexHeight - m_radicandLayout->baseline() - k_radixLineThickness - k_heightMargin,
                          k_radixLineThickness,
@@ -69,7 +75,7 @@ void NthRootLayout::render(KDContext * ctx, KDPoint p, KDColor expressionColor,
 
 KDSize NthRootLayout::computeSize() {
   KDSize radicandSize = m_radicandLayout->size();
-  KDSize indexSize = m_indexLayout->size();
+  KDSize indexSize = m_indexLayout != nullptr ? m_indexLayout->size() : KDSize(k_leftRadixWidth,0);
   return KDSize(
       indexSize.width() + 3*k_widthMargin + 2*k_radixLineThickness + radicandSize.width(),
       m_baseline + radicandSize.height() - m_radicandLayout->baseline() + k_heightMargin
@@ -79,9 +85,9 @@ KDSize NthRootLayout::computeSize() {
 ExpressionLayout * NthRootLayout::child(uint16_t index) {
   switch (index) {
     case 0:
-      return m_indexLayout;
-    case 1:
       return m_radicandLayout;
+    case 1:
+      return m_indexLayout;
     default:
       return nullptr;
   }
@@ -90,7 +96,7 @@ ExpressionLayout * NthRootLayout::child(uint16_t index) {
 KDPoint NthRootLayout::positionOfChild(ExpressionLayout * child) {
   KDCoordinate x = 0;
   KDCoordinate y = 0;
-  KDSize indexSize = m_indexLayout->size();
+  KDSize indexSize = m_indexLayout != nullptr ? m_indexLayout->size() : KDSize(k_leftRadixWidth,0);
   if (child == m_indexLayout) {
     x = 0;
     y = m_baseline - indexSize.height() -  k_indexHeight;
diff --git a/poincare/src/naperian_logarithm.cpp b/poincare/src/naperian_logarithm.cpp
new file mode 100644
index 000000000..632df69c4
--- /dev/null
+++ b/poincare/src/naperian_logarithm.cpp
@@ -0,0 +1,31 @@
+#include <poincare/naperian_logarithm.h>
+extern "C" {
+#include <assert.h>
+#include <math.h>
+#include <stdlib.h>
+}
+#include "layout/horizontal_layout.h"
+#include "layout/parenthesis_layout.h"
+#include "layout/string_layout.h"
+
+NaperianLogarithm::NaperianLogarithm() :
+  Function("ln")
+{
+}
+
+Expression::Type NaperianLogarithm::type() const {
+  return Type::NaperianLogarithm;
+}
+
+Expression * NaperianLogarithm::cloneWithDifferentOperands(Expression** newOperands,
+        int numberOfOperands, bool cloneOperands) const {
+  assert(numberOfOperands == 1 || numberOfOperands == 2);
+  assert(newOperands != nullptr);
+  NaperianLogarithm * l = new NaperianLogarithm();
+  l->setArgument(newOperands, numberOfOperands, cloneOperands);
+  return l;
+}
+
+float NaperianLogarithm::approximate(Context& context) const {
+  return log10f(m_args[0]->approximate(context))/log10f(M_E);
+}
diff --git a/poincare/src/square_root.cpp b/poincare/src/square_root.cpp
new file mode 100644
index 000000000..2456de922
--- /dev/null
+++ b/poincare/src/square_root.cpp
@@ -0,0 +1,33 @@
+#include <poincare/square_root.h>
+#include "layout/nth_root_layout.h"
+
+extern "C" {
+#include <assert.h>
+#include <math.h>
+}
+
+SquareRoot::SquareRoot() :
+  Function("v")
+{
+}
+
+Expression::Type SquareRoot::type() const {
+  return Type::SquareRoot;
+}
+
+Expression * SquareRoot::cloneWithDifferentOperands(Expression** newOperands,
+        int numberOfOperands, bool cloneOperands) const {
+  assert(numberOfOperands == 1);
+  assert(newOperands != nullptr);
+  SquareRoot * sr = new SquareRoot();
+  sr->setArgument(newOperands, numberOfOperands, cloneOperands);
+  return sr;
+}
+
+float SquareRoot::approximate(Context& context) const {
+  return powf(m_args[0]->approximate(context), 1.0f/2.0f);
+}
+
+ExpressionLayout * SquareRoot::createLayout() const {
+  return new NthRootLayout(m_args[0]->createLayout(),nullptr);
+}
\ No newline at end of file
diff --git a/poincare/src/symbol.cpp b/poincare/src/symbol.cpp
index 33aefd4c1..720040800 100644
--- a/poincare/src/symbol.cpp
+++ b/poincare/src/symbol.cpp
@@ -35,6 +35,9 @@ ExpressionLayout * Symbol::createLayout() const {
   if (m_name == SpecialSymbols::Ans) {
     return new StringLayout("ans", 4);
   }
+  if (m_name == SpecialSymbols::Pi) {
+    return new StringLayout("Pi", 4);
+  }
   return new StringLayout(&m_name, 1);
 }