Question

find the value of [625]1/4

Answer 1

First, we will check what are the factors of 625

625 = 5×5×5×5 = 5^4

Thus ,
625^(1/4) = (5^4)^(1/4) = 5

Thus, fourth-root (625) = 5

Answer 2

$\displaystyle \sf{ {(625)}^{ \frac{1}{4} } } = 5$

Given :

The expression $\displaystyle \sf{ {(625)}^{ \frac{1}{4} } }$

To find :

The value of the expression

Solution :

Step 1 of 2 :

Write down 625 in exponent form

On prime factorisation of 625 we get

625 = 5 × 5 × 5 × 5

∴ 625 = 5⁴

Step 2 of 2 :

Find the value of the expression

$\displaystyle \sf{ {(625)}^{ \frac{1}{4} } }$

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

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

$\displaystyle \sf{ = {(5)}^{1 } }$

$\displaystyle \sf{ =5}$

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