How do you find the value of 3 square root of 125?

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How do you find the value of 3 square root of 125?

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Answer 1 · 2015-09-09T11:50:37

$3 \times \sqrt{125} = 15 \sqrt{5}$ $3 xx sqrt125 = 15sqrt5$ and $\sqrt[3]{125} = 5$ $root(3)125 = 5$

Explanation:

I have heard many students read $\sqrt[3]{n}$ $root(3)n$ as "the third square root of n". This is a mistake. The square root is $\sqrt[2]{n}$ $root(2)n$ (usually denoted $\sqrt{x}$ $sqrtx$ ), the third (or cube) root is $\sqrt[3]{n}$ $root(3)n$ , the fourth root is $\sqrt[4]{n}$ $root(4)n$ and so on.

Whichever was meant the first step for simplifying is the same. Factor the radicand (the thing under the root symbol)

$125 = 5 \times 25 = 5 \times 5 \times 5 = 5^{3}$ $125 = 5xx25 = 5xx5xx5 = 5^3$

so

$3 \sqrt{125} = 3 \times \sqrt{25 \times 5} = 3 \times \sqrt{25} \times \sqrt{5} = 3 \times 5 \times \sqrt{5} = 15 \sqrt{5}$ $3sqrt125 =3 xx sqrt (25xx5) = 3xx sqrt25 xx sqrt5 = 3xx5xx sqrt5 = 15sqrt5$

And

$\sqrt[3]{125} = \sqrt[3]{5^{3}} = 5$ $root(3)125 = root(3) (5^3) = 5$

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How do you find the value of 3 square root of 125?

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