Question

3. The rationalising factor of 7√a⁴b³c⁵ is (a) 7√a³b³c² (b) 7√a²b⁴c² (c) 7√a²b³c³ (d)7√a²b⁴c³​

Answer 1

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Answer 2

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

To find: the rationalizing factor .

Solution:

Know that if the product of two surds is rational then each is called a rationalizing factor of each other.

Find the rationalizing factor of $\[\sqrt[7]{{{a^4}{b^3}{c^5}}}\]$.

Understand that to rationalize the seventh root must be removed.

Mutiply the $\[\sqrt[7]{{{a^3}{b^4}{c^2}}}\]$by its factor to make it $abc.$

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

Hence, Rationalizing factor of $\[\sqrt[7]{{{a^4}{b^3}{c^5}}}\]$ is $\[\sqrt[7]{{{a^3}{b^4}{c^2}}}\]$.