Question

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Answer 1

A =( (2+√3)/(2-√3))^1/16

= ((2+√3)^2)^1/16

= (2+√3)^1/8

A^8 = 2+√3

Answer 2

Hi there!
Here's the answer:

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• $(a^{m})^{n} = a^{mn}$

=> √√√√x = $x^{(\frac{1}{16})}$

• $(a + b) (a - b) = (a^{2} - b^{2})$

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SOLUTION:

√√√√(2+√3) = (2 + √3)^{1/16}
//y √√√√√(2 - √3) = (2 - √3)^{1/16)

A = (2 + √3)^(1/16) / (2 - √3)^(1/16)

= [ (2 + √3)/(2 - √3) ]^(1/16)

Rationalise the Numerator
= [(2 + √3) (2 + √3)] ÷ [(2 - √3) (2 + √3)]^(1/16)

= { [2 + √3]^{2} ÷ [4 - 3] }^(1/16)

={ [2 + √3]^(2) }^(1/16)

= (2 + √3)^ (1/8)

Now,
A^8 = [( 2 + √3 )^(1/8)]^8

=>A^8 = (2 + √3)

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Hope it helps