Question

If the square root of a number is between 6 and 7, then its cube root lies between:

• A. 2 and 3
• B. 2.5 and 3
• C. 3 and 4
• D. 4 and 4.5

Answer 1

The correct option is C 3 and 4

Let the given number be x
$\Rightarrow 6<\sqrt{x}<7$
(Squaring the whole inequality)
$\Rightarrow$ 36 < x < 49
(Taking cube roots of the inequality)
$\Rightarrow (36{)}^{\frac{1}{3}}<(x{)}^{\frac{1}{3}}<(49{)}^{\frac{1}{3}}$
We know, ${27}^{\frac{1}{3}}=3<{36}^{\frac{1}{3}}\&{49}^{\frac{1}{3}}<{64}^{\frac{1}{3}}=4$
$\Rightarrow 3<x^{\frac{1}{3}}<4$
$\therefore$ Cube root of x lies between 3 and 4.