Algebra Examples

$\sqrt{{(x + 5)}^{6}}$

Step 1

Rewrite ${(x + 5)}^{6}$ as ${({(x + 5)}^{3})}^{2}$ .

$\sqrt{{({(x + 5)}^{3})}^{2}}$

Step 2

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

${(x + 5)}^{3}$

Step 3

Use the Binomial Theorem.

$x^{3} + 3 x^{2} \cdot 5 + 3 x \cdot 5^{2} + 5^{3}$

Step 4

Simplify each term.

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Step 4.1

Multiply $5$ by $3$ .

$x^{3} + 15 x^{2} + 3 x \cdot 5^{2} + 5^{3}$

Step 4.2

Raise $5$ to the power of $2$ .

$x^{3} + 15 x^{2} + 3 x \cdot 25 + 5^{3}$

Step 4.3

Multiply $25$ by $3$ .

$x^{3} + 15 x^{2} + 75 x + 5^{3}$

Step 4.4

Raise $5$ to the power of $3$ .

$x^{3} + 15 x^{2} + 75 x + 125$