Precalculus Examples

$\sqrt{27 \sqrt{81 x^{8} y^{6}}}$

Step 1

Rewrite $81 x^{8} y^{6}$ as ${(9 x^{4} y^{3})}^{2}$ .

$\sqrt{27 \sqrt{{(9 x^{4} y^{3})}^{2}}}$

Step 2

Pull terms out from under the radical, assuming positive real numbers.

$\sqrt{27 \cdot 9 x^{4} y^{3}}$

Step 3

Multiply $27$ by $9$ .

$\sqrt{243 x^{4} y^{3}}$

Step 4

Rewrite $243 x^{4} y^{3}$ as ${(9 x^{2} y)}^{2} \cdot (3 y)$ .

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Step 4.1

Factor $81$ out of $243$ .

$\sqrt{81 (3) x^{4} y^{3}}$

Step 4.2

Rewrite $81$ as $9^{2}$ .

$\sqrt{9^{2} \cdot 3 x^{4} y^{3}}$

Step 4.3

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

$\sqrt{9^{2} \cdot 3 {(x^{2})}^{2} y^{3}}$

Step 4.4

Factor out $y^{2}$ .

$\sqrt{9^{2} \cdot 3 {(x^{2})}^{2} (y^{2} y)}$

Step 4.5

Move $3$ .

$\sqrt{9^{2} {(x^{2})}^{2} y^{2} \cdot 3 y}$

Step 4.6

Rewrite $9^{2} {(x^{2})}^{2} y^{2}$ as ${(9 x^{2} y)}^{2}$ .

$\sqrt{{(9 x^{2} y)}^{2} \cdot 3 y}$

Step 4.7

Add parentheses.

$\sqrt{{(9 x^{2} y)}^{2} \cdot (3 y)}$

Step 5

Pull terms out from under the radical.

$9 x^{2} y \sqrt{3 y}$