Numbers - Square Root

SOURCE:COMPETITION
Number of Problems: 4. : (Book)

1.

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Simplify $sqrt[3]{xsqrt[3]{xsqrt[3]{xsqrt{x}}}}$ .

$mathrm{(A) } sqrt{x}qquad mathrm{(B) } sqrt[3]{x^{2}}qquad mathrm{(C) } sqrt[27]{x^{2}}qquad mathrm{(D) } ...$

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2.

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Which of the following is equivalent to $sqrt{frac{x}{1-frac{x-1}{x}}}$ when $x < 0$ ?

$mathrm{(A) } -xqquad mathrm{(B) } xqquad mathrm{(C) } 1qquad mathrm{(D) } sqrt{frac{x}{2}}qquad mathrm{(E)...$

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3.

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Assume that $x$ is a positive real number. Which is equivalent to $sqrt[3]{xsqrt{x}}$ ?

$mathrm{(A)} x^{1/6}qquadmathrm{(B)} x^{1/4}qquadmathrm{(C)} x^{3/8}qquadmathrm{(D)} x^{1/2}qquadmathrm{(E)} x$

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4.

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What is the product of all the roots of the equation $sqrt{5 | x | + 8} = sqrt{x^2 - 16}.$

$extbf{(A)} -64 qquad extbf{(B)} -24 qquad extbf{(C)} -9 qquad extbf{(D)} 24 qquad extbf{(E)} 576$

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