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Show, without using a calculator, that $ \sqrt[12]{10} \times \sqrt[6]{640} \times \sqrt[4]{810} \times \sqrt{40} =120$
in Mathematics by Diamond (75,934 points) | 100 views

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apply surd and exponent laws, and split the numbers into bases which simplifies with their nth roots

=10^1/12 x 6throot(64x10) x 4throot(81x10)  x sqroot(4x10)

= 10^1/12 x 6throot(2^6 x 10) x 4throot(3^4 x 10)  x sqroot(2^2 x 10)

= 10^1/12 x 2^6/6 x 10^1/6 x 3^4/4 x 10^1/4 x 2^2/2 x 10^1/2  , then simplify and add exponents for same bases,

= 2^2 x 3 x 10^12/12

= 120 , shown.
by Diamond (43,720 points)

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