Algebra Examples

{(2 \sqrt{5})}^{2}

${(2 \sqrt{5})}^{2}$

Step 1

Simplify the expression.

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Step 1.1

Apply the product rule to

2 \sqrt{5}

$2 \sqrt{5}$ .

2^{2} {\sqrt{5}}^{2}

$2^{2} {\sqrt{5}}^{2}$

Step 1.2

Raise

2

$2$ to the power of

2

$2$ .

4 {\sqrt{5}}^{2}

$4 {\sqrt{5}}^{2}$

4 {\sqrt{5}}^{2}

$4 {\sqrt{5}}^{2}$

Step 2

Rewrite

{\sqrt{5}}^{2}

${\sqrt{5}}^{2}$ as

5

$5$ .

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Step 2.1

Use

\sqrt[n]{a^{x}} = a^{\frac{x}{n}}

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite

\sqrt{5}

$\sqrt{5}$ as

5^{\frac{1}{2}}

$5^{\frac{1}{2}}$ .

4 {(5^{\frac{1}{2}})}^{2}

$4 {(5^{\frac{1}{2}})}^{2}$

Step 2.2

Apply the power rule and multiply exponents,

{(a^{m})}^{n} = a^{m n}

${(a^{m})}^{n} = a^{m n}$ .

4 \cdot 5^{\frac{1}{2} \cdot 2}

$4 \cdot 5^{\frac{1}{2} \cdot 2}$

Step 2.3

Combine

\frac{1}{2}

$\frac{1}{2}$ and

2

$2$ .

4 \cdot 5^{\frac{2}{2}}

$4 \cdot 5^{\frac{2}{2}}$

Step 2.4

Cancel the common factor of

2

$2$ .

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Step 2.4.1

Cancel the common factor.

$4 \cdot 5^{\frac{2}{2}}$

Step 2.4.2

Rewrite the expression.

$4 \cdot 5^{1}$

$4 \cdot 5^{1}$

Step 2.5

Evaluate the exponent.

$4 \cdot 5$

$4 \cdot 5$

Step 3

Multiply

$4$ by

$5$ .

$20$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$