Question

why it is cube root 16 and not cube root 4 to rationlize denometer sir? please explain the logic for this thanks ma'am

20 points big prize - brainlist

Answer 1

Step-by-step explanation:

$Given:k=\sqrt[3]{\frac{25*25*5*5}{4}}$

$=>k=\frac{25}{\sqrt[3]{4}}$

On rationalizing the denominator, we get

$=>k=\frac{25}{\sqrt[3]{4}}*\frac{4^{\frac{2}{3}}}{4^{\frac{2}{3}}}$

$=>k=\frac{25*4^{\frac{2}{3}}}{\sqrt[3]{4}*4^{\frac{2}{3}}}$

$=>k=\frac{25*4^{\frac{2}{3}}}{4^{\frac{1}{3} + \frac{2}{3}}}$

$=>k=\frac{25*(2^{2})^\frac{2}{3}}{4^1}$

$=>k=\frac{25*2^{\frac{4}{3}}}{4}$

$=>k=\frac{25*2^{1 + \frac{1}{3}}}{2^2}$

$=>k=\frac{25*2*2^{\frac{1}{3}}}{2^2}$

$=>k=\frac{25*2^{\frac{1}{3}}}{2}$

$=>k=\boxed{\frac{25\sqrt[3]{2}}{2}}$

Hope it helps!