Question

The rationalising factor ⁷√a⁴,b³,c⁵​

Answer 1

Given :   ⁷√a⁴,b³,c⁵​

$\sqrt[7]{a^4b^3c^5}$

To Find : rationalizing factor

Solution

$\sqrt[7]{a^4b^3c^5}$

rationalizing factor :

The factor of multiplication by which an irrational number is multiplied to convert it into rational number

If the product of two irrational numbers or surds is a rational number, then each surd is a rationalizing factor for each other.

as there is 7th root so we need to have power of a , b and c as 7 inside 7th root

a⁷/a⁴ = a³

b⁷/b³ = b⁴

c⁷/c⁵ = c²

so rationalizing factor is

$\sqrt[7]{a^3b^4c^2}$

$\sqrt[7]{a^4b^3c^5}$ * $\sqrt[7]{a^3b^4c^2}$  = abc

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