Algebra Examples

$\sqrt{{(y - 6)}^{8}}$

Step 1

Rewrite ${(y - 6)}^{8}$ as ${({(y - 6)}^{4})}^{2}$ .

$\sqrt{{({(y - 6)}^{4})}^{2}}$

Step 2

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

${(y - 6)}^{4}$

Step 3

Use the Binomial Theorem.

$y^{4} + 4 y^{3} \cdot - 6 + 6 y^{2} {(- 6)}^{2} + 4 y {(- 6)}^{3} + {(- 6)}^{4}$

Step 4

Simplify each term.

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Step 4.1

Multiply $- 6$ by $4$ .

$y^{4} - 24 y^{3} + 6 y^{2} {(- 6)}^{2} + 4 y {(- 6)}^{3} + {(- 6)}^{4}$

Step 4.2

Raise $- 6$ to the power of $2$ .

$y^{4} - 24 y^{3} + 6 y^{2} \cdot 36 + 4 y {(- 6)}^{3} + {(- 6)}^{4}$

Step 4.3

Multiply $36$ by $6$ .

$y^{4} - 24 y^{3} + 216 y^{2} + 4 y {(- 6)}^{3} + {(- 6)}^{4}$

Step 4.4

Raise $- 6$ to the power of $3$ .

$y^{4} - 24 y^{3} + 216 y^{2} + 4 y \cdot - 216 + {(- 6)}^{4}$

Step 4.5

Multiply $- 216$ by $4$ .

$y^{4} - 24 y^{3} + 216 y^{2} - 864 y + {(- 6)}^{4}$

Step 4.6

Raise $- 6$ to the power of $4$ .

$y^{4} - 24 y^{3} + 216 y^{2} - 864 y + 1296$