Exercice 6

Question

Écrire sous la forme \(a\sqrt{b}\) où a et b sont des nombres entiers strictement positifs, b étant le plus petit possible :

  1. \(\sqrt{50}\)

  2. \(\sqrt{200}\)

  3. \(\sqrt{147}\)

  4. \(\sqrt{54}\)

Solution

Question 1

\(\sqrt{50} = \sqrt{25 \times 2} = \sqrt{5^2 \times 2} = \sqrt{5^2} \times \sqrt{2} = \color{red}5\sqrt{2}\)

Question 2

\(\sqrt{200} = \sqrt{100 \times 2} = \sqrt{10^2 \times 2} = \sqrt{10^2} \times \sqrt{2} = \color{red}10\sqrt{2}\)

Question 3

\(\sqrt{147} = \sqrt{49 \times 3} = \sqrt{7^2 \times 3} = \sqrt{7^2} \times \sqrt{3} = \color{red}7\sqrt{3}\)

Question 4

\(\sqrt{54} = \sqrt{9 \times 6} = \sqrt{3^2 \times 6} = \sqrt{3^2} \times \sqrt{6} = \color{red}3\sqrt{6}\)