Question

What is (sqrt2+sqrt8+sqrt18+sqrt32) to the second power P.S. not 60

Answer 1

Answer: 200

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Work Shown:

One approach is to simplify the stuff under the second power exponent. After that simplification, you would then square the result.

`x = √(2)+√(8)+√(18)+√(32)\\\\x = √(2)+√(4*2)+√(9*2)+√(16*2)\\\\x = √(2)+√(4)*√(2)+√(9)*√(2)+√(16)*√(2)\\\\x = 1√(2)+2√(2)+3√(2)+4√(2)\\\\x = (1+2+3+4)√(2)\\\\x = 10√(2)\\\\x^2 = \left(10√(2)\right)^2\\\\x^2 = \left(10√(2)\right)*\left(10√(2)\right)\\\\x^2 = 10*10√(2)*√(2)\\\\x^2 = 100√(2*2)\\\\x^2 = 100√(4)\\\\x^2 = 100*2\\\\x^2 = 200\\\\`

So,

`\left(√(2)+√(8)+√(18)+√(32)\right)^2 = 200`

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Checking the answer:

Using a calculator,

sqrt(2)+sqrt(8)+sqrt(18)+sqrt(32) = 14.142135623731

Then you square that to get (14.142135623731)^2 = 200.000000000001

Your calculator may not have that 1 at the end. It shouldn't be there and it's a result of rounding error. But it's close enough to 200.

Answer 2

to solve that it gonna be 10 square root of 2 and in decimal form it gonna be 14.14213562

Hope this helps

Explanation: