Algebra Examples

$f (x) = \sqrt{216 a^{6} b^{8}}$

Step 1

Write $f (x) = \sqrt{216 a^{6} b^{8}}$ as an equation.

$y = \sqrt{216 a^{6} b^{8}}$

Step 2

Simplify $\sqrt{216 a^{6} b^{8}}$ .

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Step 2.1

Rewrite $216 a^{6} b^{8}$ as ${(6 a^{3} b^{4})}^{2} \cdot 6$ .

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Step 2.1.1

Factor $36$ out of $216$ .

$y = \sqrt{36 (6) a^{6} b^{8}}$

Step 2.1.2

Rewrite $36$ as $6^{2}$ .

$y = \sqrt{6^{2} \cdot 6 a^{6} b^{8}}$

Step 2.1.3

Rewrite $a^{6}$ as ${(a^{3})}^{2}$ .

$y = \sqrt{6^{2} \cdot 6 {(a^{3})}^{2} b^{8}}$

Step 2.1.4

Rewrite $b^{8}$ as ${(b^{4})}^{2}$ .

$y = \sqrt{6^{2} \cdot 6 {(a^{3})}^{2} {(b^{4})}^{2}}$

Step 2.1.5

Move $6$ .

$y = \sqrt{6^{2} {(a^{3})}^{2} {(b^{4})}^{2} \cdot 6}$

Step 2.1.6

Rewrite $6^{2} {(a^{3})}^{2} {(b^{4})}^{2}$ as ${(6 a^{3} b^{4})}^{2}$ .

$y = \sqrt{{(6 a^{3} b^{4})}^{2} \cdot 6}$

Step 2.2

Pull terms out from under the radical.

$y = 6 a^{3} b^{4} \sqrt{6}$