A number whose square root is twice its cubic root is36-64-25-16-

The correct option is B 64 Let the number be x Given √(x) = 2√(x) x^1/2 = 2x^1/3 x^1/2/x^1/3 = 2 x^1/6 = 2 Therefore, x^ (1/6)^6= 2^6 ⇒ x = 64 ∴ The required ...

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Standard VIII

Mathematics

Cube Root Using Prime Factorisation

A number whos...

Question

A number whose square root is twice its cubic root is

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Solution

The correct option is B
64

Let the number be $x$

Given $\sqrt{x} = 2 \sqrt[3]{x}$
$x^{\frac{1}{2}} = 2 x^{\frac{1}{3}}$
$\frac{x^{\frac{1}{2}}}{x^{\frac{1}{3}}} = 2$
$x^{\frac{1}{6}} = 2$

Therefore,
$x^{(\frac{1}{6})^{6}} = 2^{6}$
$\Rightarrow x = 64$

$∴$ The required number is 64

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A number whose square root is twice its cubic root is

The correct option is B 64 Let the number be x Given √x=23√x x12=2x13 x12x13=2 x16=2 Therefore, x(16)6=26 ⇒x=64 ∴ The required number is 64

The correct option is B
64

Let the number be $x$

Given $\sqrt{x} = 2 \sqrt[3]{x}$
$x^{\frac{1}{2}} = 2 x^{\frac{1}{3}}$
$\frac{x^{\frac{1}{2}}}{x^{\frac{1}{3}}} = 2$
$x^{\frac{1}{6}} = 2$

Therefore,
$x^{(\frac{1}{6})^{6}} = 2^{6}$
$\Rightarrow x = 64$

$∴$ The required number is 64