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Maths-

SAT

Easy

Question

Which of the following is equivalent to $fourth root of x squared plus 8 x plus 16 end root$ , where x>0?

(x+4)⁴
(x+4)²
(x+4)
$(x + 4)^{\frac{1}{2}}$

The correct answer is: $left parenthesis x plus 4 right parenthesis to the power of 1 half end exponent$

$fourth root of x squared plus 8 x plus 16 end root equals fourth root of x squared plus 2 left parenthesis 4 right parenthesis left parenthesis x right parenthesis plus 4 squared end root$
$equals fourth root of left parenthesis x plus 4 right parenthesis squared end root equals left parenthesis x plus 4 right parenthesis to the power of 2 divided by 4 end exponent space space equals left parenthesis x plus 4 right parenthesis to the power of 1 divided by 2 end exponent$

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