Simplify each of the following:$ \frac{\sqrt[4]{1250}}{\sqrt[4]{2}} $

Given:

\( \frac{\sqrt[4]{1250}}{\sqrt[4]{2}} \)

To do: 

We have to simplify the given expression.

Solution:

We know that,

$(a^{m})^{n}=a^{m n}$

$a^{m} \times a^{n}=a^{m+n}$

$a^{m} \div a^{n}=a^{m-n}$

$\sqrt[n]{a} \times \sqrt[n]{b}=\sqrt[n]{a \times b}$

$\sqrt[n]{a} \div \sqrt[n]{b}=\sqrt[n]{\frac{a}{b}}$

$a^{0}=1$

Therefore,

$\frac{\sqrt[4]{1250}}{\sqrt[4]{2}}=\sqrt[4]{\frac{1250}{2}}$

$=\sqrt[4]{625}$

$=\sqrt[4]{5 \times 5 \times 5 \times 5}$

$=(5^{4})^{\frac{1}{4}}$

$=5^{4 \times \frac{1}{4}}$

$=5^{1}$

$=5$

Hence, $\frac{\sqrt[4]{1250}}{\sqrt[4]{2}}=5$. 

Tutorialspoint

Updated on: 10-Oct-2022

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