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Multiplication of Numbers with Square Roots

Simplify:√12×...

Question

Simplify:-

⁴√12×⁷√6

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Solution

12^(1/4)=(223)^(1/4)

6^(1/7)=(23)^(1/7)

12^(1/4)6^(1/7)
=(223)^(1/4) (23)^(1/7)
=(2²3)^(1/4)
(2^1/7)(3^1/7)

=(2²^1/4)(3^1/4)(2^1/7)(3^1/7)

=2^(9/14) * 3^(11/28)
=2^(18/28)3^(11/28)
=(2^18 3^11)^(1/28)

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