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Maths-

General

Easy

Question

Which of the following is equivalent to $4 square root of left parenthesis x squared plus 8 x plus 16 right parenthesis end root$ , where x > 0 ?

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

The correct answer is: $open parentheses x plus 4 close parentheses to the power of 1 half end exponent$

Hint:-
We simplify the given expression and find the solution.
Step-by-step solution:-
$4 square root of open parentheses x squared plus 8 x plus 16 close parentheses end root equals space 4 square root of open parentheses x squared plus 8 x plus 16 close parentheses end root 4 square root of open parentheses left parenthesis x right parenthesis squared plus 2 left parenthesis 4 right parenthesis left parenthesis x right parenthesis plus left parenthesis 4 right parenthesis squared close parentheses end root 4 square root of open parentheses x plus 4 close parentheses squared end root space minus negative negative negative negative negative negative negative negative negative negative negative negative negative space left square bracket left parenthesis a plus b right parenthesis squared space equals space a to the power of 2 space end exponent plus space 2 a b space plus space b squared right square bracket left parenthesis open parentheses x plus 4 close parentheses squared right parenthesis to the power of 1 fourth end exponent open parentheses x plus 4 close parentheses to the power of 2 cross times fraction numerator 1 over denominator 4 end fraction end exponent minus negative negative negative negative negative negative negative negative negative negative space left parenthesis F r a c t i o n a l space e x p o n e n t s right parenthesis$
= $open parentheses x plus 4 close parentheses to the power of 1 half end exponent$
Final Answer:-
Option D i.e. $open parentheses x plus 4 close parentheses to the power of 1 half end exponent$ is the correct Option.

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