If 5 √(3)+√(75) = 17.32, then the value of 14 √(3)+√(108) is:

If 5 √(3)+√(75) = 17.32, then the value of 14 √(3)+√(108)…

If 5 $\sqrt{3}+\sqrt{75}$ = 17.32, then the value of 14 $\sqrt{3}+\sqrt{108}$ is:

Show answer & explanation

Correct answer: C

Explanation

The correct answer is option 3 i.e. 34.64.

5 $\sqrt{3}+\sqrt{75}$ = 17.32 ⇒ 5(3)^1/2+ 5(3)^1/2= 17.32

So, 10(3)^1/2= 17.32

14 $\sqrt{3}+\sqrt{108}$ = 14(3)^1/2 + (36 × 3)^1/2

⇒ 14 $\sqrt{3}+\sqrt{108}$ = 14(3)^1/2 + 6(3)^1/2 = 20(3)^1/2

So, 20(3)^1/2 = 2 × 10(3)^1/2= 2 × 17.32 = 34.64