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Rationalising factor of 403\sqrt[3]{40}340​​ is:
Question

Rationalising factor of 403\sqrt[3]{40}​ is:

A.

101310^{\frac{1}{3}}​​

B.

5235^{\frac{2}{3}}​​

C.

401340^{\frac{1}{3}}​​

D.

2232^{\frac{2}{3}}​​

Correct option is B

Given:
The expression: 403\sqrt[3]{40}​​
Solution:
40 =8×5=23×5 8 \times 5 = 2^3 \times 5 ​​
403=23×53=2×53\sqrt[3]{40} = \sqrt[3]{2^3 \times 5} = 2 \times \sqrt[3]{5} ​​
Rationalizing factor
To rationalize 53 \sqrt[3]{5}​, multiply it by 523\sqrt[3]{5^2}​ (since 5×52=53=1255 \times 5^2 = 5^3 = 125​, a perfect cube).
Rationalizing factor = 523=523\sqrt[3]{5^2} = 5^\frac 23


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