What is $3 \sqrt{8^{2}}$ $3sqrt(8^2)$ ?

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What is $3 \sqrt{8^{2}}$ $3sqrt(8^2)$ ?

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Answer 1 · 2017-08-31T15:17:46

$3 \cdot \sqrt{8^{2}} = 24$ $3*sqrt(8^2) = 24$

Explanation:

We need to find $3 \cdot \sqrt{8^{2}}$ $3*sqrt(8^2)$ . Since squaring and square rooting are inverse functions, they cancel out, leaving just $3 \cdot 8 = 24$ $3*8=24$ .

Answer 2 · 2017-08-31T15:24:15

$\sqrt[3]{8^{2}} = 4$ $root(3)(8^2) = 4$

Explanation:

Assuming the intended expression was $\sqrt[3]{8^{2}}$ $root(3)(8^2)$ , we find:

$\sqrt[3]{8^{2}} = \sqrt[3]{{(2^{3})}^{2}} = \sqrt[3]{{(2^{2})}^{3}} = 2^{2} = 4$ $root(3)(8^2) = root(3)((2^3)^2) = root(3)((2^2)^3) = 2^2 = 4$

Answer 3 · 2017-08-31T20:47:14

Assuming $\sqrt[3]{8^{2}}$ $root3(8^2)$ , we could also write this as:

$\sqrt[3]{8^{2}} = 8^{\frac{2}{3}} = {(2^{3})}^{\frac{2}{3}} = 2^{2} = 4$ $root3(8^2)=8^(2/3)=(2^3)^(2/3)=2^2=4$

This used:

$\sqrt[b]{x^{a}} = x^{\frac{a}{b}}$ $rootb(x^a)=x^(a/b)$
${(x^{a})}^{b} = x^{a b}$ $(x^a)^b=x^(ab)$

And the ability to prime factorize, that is, know that $8 = 2 \cdot 2 \cdot 2 = 2^{3}$ $8=2*2*2=2^3$ .

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What is $3 \sqrt{8^{2}}$ $3sqrt(8^2)$ ?

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