Question #acf06

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Question #acf06

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Answer 1 · 2018-02-24T02:45:54

Answer: $5 {(x + 2)}^{2}$ $5(x+2)^2$

Explanation:

Assuming question is asking for $\sqrt{25 {(x + 2)}^{4}}$ $sqrt(25(x+2)^4)$

By definition of square root, we know that:
$\sqrt{p^{2}} = p$ $sqrt(p^2)=p$ , where $p$ $p$ is any function

Therefore, applying this definition to the original problem we can see that the original problem can be factored into the form $p^{2}$ $p^2$ :
$\sqrt{25 {(x + 2)}^{4}}$ $sqrt(25(x+2)^4)$
$= \sqrt{5 \cdot 5 \cdot {(x + 2)}^{2} \cdot {(x + 2)}^{2}}$ $=sqrt(5*5*(x+2)^2*(x+2)^2)$
$= \sqrt{5^{2} \cdot {({(x + 2)}^{2})}^{2}}$ $=sqrt(5^2*((x+2)^2)^2)$
$= \sqrt{{(5 {(x + 2)}^{2})}^{2}}$ $=sqrt((5(x+2)^2)^2)$

Now, we can set our $p$ $p$ to be $p = 5 {(x + 2)}^{2}$ $p=5(x+2)^2$ , so our answer is
$5 {(x + 2)}^{2}$ $5(x+2)^2$

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Question #acf06

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