Basic Math Examples

$\sqrt{32 a} - \sqrt{2 a}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $32 a$ as ${(2^{2})}^{2} \cdot (2 a)$ .

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Step 1.1.1

Factor $16$ out of $32$ .

$\sqrt{16 (2) a} - \sqrt{2 a}$

Step 1.1.2

Rewrite $16$ as $4^{2}$ .

$\sqrt{4^{2} \cdot 2 a} - \sqrt{2 a}$

Step 1.1.3

Rewrite $4$ as $2^{2}$ .

$\sqrt{{(2^{2})}^{2} \cdot 2 a} - \sqrt{2 a}$

Step 1.1.4

Add parentheses.

$\sqrt{{(2^{2})}^{2} \cdot (2 a)} - \sqrt{2 a}$

$\sqrt{{(2^{2})}^{2} \cdot (2 a)} - \sqrt{2 a}$

Step 1.2

Pull terms out from under the radical.

$2^{2} \sqrt{2 a} - \sqrt{2 a}$

Step 1.3

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

$4 \sqrt{2 a} - \sqrt{2 a}$

$4 \sqrt{2 a} - \sqrt{2 a}$

Step 2

Subtract $\sqrt{2 a}$ from $4 \sqrt{2 a}$ .

$3 \sqrt{2 a}$

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