Precalculus Examples

$\sqrt{45 x^{9 y^{7}}}$

Step 1

Rewrite $45 x^{9 y^{7}}$ as $3^{2} \cdot (5 x^{3^{2} y^{7}})$ .

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Step 1.1

Factor $9$ out of $45$ .

$\sqrt{9 (5) x^{9 y^{7}}}$

Step 1.2

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2} \cdot 5 x^{9 y^{7}}}$

Step 1.3

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2} \cdot 5 x^{3^{2} y^{7}}}$

Step 1.4

Add parentheses.

$\sqrt{3^{2} \cdot (5 x^{3^{2} y^{7}})}$

Step 2

Pull terms out from under the radical.

$3 \sqrt{5 x^{3^{2} y^{7}}}$

Step 3

Raise $3$ to the power of $2$ .

$3 \sqrt{5 x^{9 y^{7}}}$