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${:[root(4)(25m^(2))=root(2)(25 m)],[=5m]:}$

$34$ . $\newline$ $\begin{aligned} \sqrt[4]{25 m^{2}} & =\sqrt[2]{25 m} \\ & =5 m \end{aligned}$

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Find higher derivatives of rational and radical functions

Full solution

Q.

34

.

\newline

\begin{aligned} \sqrt[4]{25 m^{2}} & =\sqrt[2]{25 m} \\ & =5 m \end{aligned}

Given Expression: We are given the expression $\sqrt[4]{25m^2}$ and we need to simplify it. $\newline$ The fourth root of a number is the same as raising that number to the power of $1$ / $4$ . $\newline$ So, we can rewrite the expression as $(25m^2)^{1/4}$ .
Rewriting Expression: First, we will deal with the numerical part, which is the fourth root of $25$ . $\newline$ The fourth root of $25$ is the number that when raised to the power of $4$ equals $25$ . $\newline$ Since $5^4 = 625$ and $2^4 = 16$ , we know that the fourth root of $25$ is not a whole number. However, we are looking for the square root of $25$ , which is a perfect square, and the square root of $25$ is $5$ . $\newline$ So, $\sqrt[4]{25} = \sqrt{5}$ .

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