How do you simplify $\sqrt{45 n^{5}}$ $sqrt(45n^5)$ ?

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How do you simplify $\sqrt{45 n^{5}}$ $sqrt(45n^5)$ ?

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Answer 1 · 2016-05-16T17:41:13

$= 3 n^{2} \sqrt{5 n}$ $=3n^2sqrt (5n)$

Explanation:

$\sqrt{45 n^{5}}$ $sqrt (45n^5$

Prime factorising $45 :$ $45:$

$45 = 3 \cdot 3 \cdot 5 = 3^{2} \cdot 5$ $45 = 3 * 3 * 5 = color(blue)(3^2) * 5$

The expression now becomes:
$\sqrt{45 n^{5}} = \sqrt{3^{2} \cdot 5 \cdot n^{2} \cdot n^{2} \cdot n}$ $sqrt (45n^5) = sqrt ( color(blue)(3^2) * 5 * color(blue)(n ^ 2 * n ^2) * n)$

$= 3 \cdot n \cdot n \sqrt{5 n}$ $=color(blue)(3 * n * n ) sqrt (5n)$

$= 3 n^{2} \sqrt{5 n}$ $=3n^2sqrt (5n)$

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How do you simplify $\sqrt{45 n^{5}}$ $sqrt(45n^5)$ ?

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How do you simplify $\sqrt{45 n^{5}}$ $sqrt(45n^5)$ ?