Exercice 2

Question

Effectuer les calculs suivants :

  1. \(\left(-\sqrt {5}~\right)^2\)

  2. \(-\left(\sqrt {\frac{3}{4}}~\right)^2\)

  3. \(\left(2\sqrt {3}~\right)^2\)

  4. \(\left(5\sqrt {3}~\right)^2\)

Indice

Bien regarder la place de la puissance par rapport à la racine carrée.

Solution

Question 1

\(\left(-\sqrt {5}~\right)^2 = (-\sqrt {5}) \times (-\sqrt {5}) = \left(\sqrt {5}~\right)^2= \color{red}5\)

Question 2

\(-\left(\sqrt {\frac{3}{4}}~\right)^2 = \color{red}-\frac{3}{4}\)

Question 3

\(\left(2\sqrt {3}~\right)^2 = 2^2 \times \left(\sqrt {3}~\right)^2 = 4 \times 3 = \color{red}12\)

Question 4

\(\left(5\sqrt {3}~\right)^2 = 5^2 \times \left(\sqrt {3}~\right)^2 = 25 \times 3 = \color{red}75\)