Question

Arrange the following irrational numbers in decending order of magnitude,

5$\sqrt{5}$ , 3$\sqrt{7}$ , 8$\sqrt{2}$ , 8

• A. (i), (ii), (iii)
• B. (i), (iii)
• C. (i), (ii)
• D. (ii), (iii)

Answer 1

The correct option is B

(i), (iii)

Writing all the square roots under one radical , we get
5$\sqrt{5}$ = $\sqrt{5\times 5\times 5}$ = $\sqrt{125}$
3$\sqrt{7}$ = $\sqrt{3\times 3\times 7}$ = $\sqrt{63}$
8$\sqrt{2}$ = $\sqrt{8\times 8\times 2}$ = $\sqrt{128}$

8 = $\sqrt{8\times 8}=\sqrt{64}$

Arranging $\sqrt{125}$ , $\sqrt{63}$ , $\sqrt{128}$, $\sqrt{64}$ in descending order , we get
$\sqrt{128}$ , $\sqrt{125}$ , $\sqrt{64}$ , $\sqrt{63}$

Hence 8$\sqrt{2}$ > 5$\sqrt{5}$ > 8 > 3$\sqrt{7}$