Algebra Examples

$\sqrt{\frac{a^{2} + b^{2}}{4}}$

Step 1

Rewrite $\frac{a^{2} + b^{2}}{4}$ as ${(\frac{1}{2})}^{2} (a^{2} + b^{2})$ .

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Step 1.1

Factor the perfect power $1^{2}$ out of $a^{2} + b^{2}$ .

$\sqrt{\frac{1^{2} (a^{2} + b^{2})}{4}}$

Step 1.2

Factor the perfect power $2^{2}$ out of $4$ .

$\sqrt{\frac{1^{2} (a^{2} + b^{2})}{2^{2} \cdot 1}}$

Step 1.3

Rearrange the fraction $\frac{1^{2} (a^{2} + b^{2})}{2^{2} \cdot 1}$ .

$\sqrt{{(\frac{1}{2})}^{2} (a^{2} + b^{2})}$

Step 2

Pull terms out from under the radical.

$\frac{1}{2} \sqrt{a^{2} + b^{2}}$

Step 3

Combine $\frac{1}{2}$ and $\sqrt{a^{2} + b^{2}}$ .

$\frac{\sqrt{a^{2} + b^{2}}}{2}$