Question

find the 5th root of 1024\3125​

Answer 1

The 5th root of (1024)/(3125) is equal to

Given:

The number is (1024)/(3125).

To Find:

The 5th root of (1024)/(3125).

Solution:

  $The\:5th\:root\:of\:1024/3125\:is \:given\:as:\\\\=\sqrt[5]{\frac{1024}{3125} }\\ \\=\sqrt[5]{\frac{4\times4\times4\times4\times4}{5\times5\times5\times5\times5} } \\\\=\sqrt[5]{\frac{4^{5} }{5^{5} } } \\\\=\sqrt[5]{(\frac{4}{5} )^{5} } \\\\=[(\frac{4}{5} )^{5}]^{\frac{1}{5} } \\\\=[(\frac{4}{5} )]^1\\\\=\frac{4}{5}$

Therefore the 5th root of (1024)/(3125) is equal to 4/5.

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Answer 2

$\displaystyle \sf \sqrt[5]{ \frac{1024}{3125} } = \frac{4}{5}$

Given :

$\displaystyle \sf \sqrt[5]{ \frac{1024}{3125} }$

To find :

The value of the expression

Solution :

Step 1 of 2 :

Write down the given expression

Here the given expression is

$\displaystyle \sf \sqrt[5]{ \frac{1024}{3125} }$

Step 2 of 2 :

Find the value of the expression

1024

= 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

= 4 × 4 × 4 × 4 × 4

= 4⁵

3125

= 5 × 5 × 5 × 5 × 5

= 5⁵

Thus we get

$\displaystyle \sf \sqrt[5]{ \frac{1024}{3125} }$

$\displaystyle \sf = \sqrt[5]{ \frac{ {4}^{5} }{ {5}^{5} } }$

$\displaystyle \sf = \sqrt[5]{ {\bigg( \frac{4}{5} \bigg)}^{5} }$

$\displaystyle \sf = \frac{4}{5}$

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Learn more from Brainly :-

$1.$ the value of (√5+√2)²

https://brainly.in/question/3299659

2. Simplify ( 8+√5)(8-√5).

https://brainly.in/question/17061574

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