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# Help:

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Help:

$$1) \sqrt{(x-1)^2} = 1 -x$$

$$2) \sqrt{(y^6)} = -y^3$$

$$3) \sqrt{(1+(\sqrt{2 + \sqrt{n})})} = 2$$

Thanks so much! Please explain. I got the answers but weren't sure if they are correct.

Jul 8, 2018

#1
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3)

Solve for n:
sqrt(sqrt(sqrt(n) + 2) + 1) = 2

Raise both sides to the power of two:
sqrt(sqrt(n) + 2) + 1 = 4

Subtract 1 from both sides:
sqrt(sqrt(n) + 2) = 3

Raise both sides to the power of two:
sqrt(n) + 2 = 9

Subtract 2 from both sides:
sqrt(n) = 7

Raise both sides to the power of two:
n = 49

Jul 8, 2018
#2
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Remember that square rooting is equivalent to raising to the power of a half.

1. The operations would cancel leaving x-1

2. This would be (y6)1/2 which, using the power law of indices, would leave y3

3. We would need to square each side, subtract 1 from each side, square each side, subtract 2 from each side and then square each side, in that order. That would leave n=49

Jul 8, 2018