Exercice 5

Question

Écrire les expressions sous la forme d'une unique racine carrée :

  1. \(2\sqrt{3}\)

  2. \(3\sqrt{2}\)

  3. \(5\sqrt{7}\)

  4. \(6\sqrt{2}\)

Solution

Question 1

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

Question 2

\(3\sqrt{2} = \sqrt{3^2} \times \sqrt{2} = \sqrt{9} \times \sqrt{2} = \sqrt{9 \times 2} = \color{red}\sqrt{18}\)

Question 3

\(5\sqrt{7} = \sqrt{5^2} \times \sqrt{7} = \sqrt{25} \times \sqrt{7} = \sqrt{25 \times 7} = \color{red}\sqrt{175}\)

Question 4

\(6\sqrt{2} = \sqrt{6^2} \times \sqrt{2} = \sqrt{36} \times \sqrt{2} = \sqrt{36 \times 2} = \color{red}\sqrt{72}\)