Basic Math Examples

$\sqrt{\frac{18}{2}} (a) = 33$

Step 1

Simplify.

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Step 1.1

Reduce the expression $\frac{18}{2}$ by cancelling the common factors.

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Step 1.1.1

Factor $2$ out of $18$ .

$\sqrt{\frac{2 \cdot 9}{2}} a = 33$

Step 1.1.2

Factor $2$ out of $2$ .

$\sqrt{\frac{2 \cdot 9}{2 (1)}} a = 33$

Step 1.1.3

Cancel the common factor.

$\sqrt{\frac{2 \cdot 9}{2 \cdot 1}} a = 33$

Step 1.1.4

Rewrite the expression.

$\sqrt{\frac{9}{1}} a = 33$

Step 1.2

Divide $9$ by $1$ .

$\sqrt{9} a = 33$

Step 2

Divide each term in $\sqrt{9} a = 33$ by $\sqrt{9}$ and simplify.

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Step 2.1

Divide each term in $\sqrt{9} a = 33$ by $\sqrt{9}$ .

$\frac{\sqrt{9} a}{\sqrt{9}} = \frac{33}{\sqrt{9}}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $\sqrt{9}$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{\sqrt{9} a}{\sqrt{9}} = \frac{33}{\sqrt{9}}$

Step 2.2.1.2

Divide $a$ by $1$ .

$a = \frac{33}{\sqrt{9}}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify the denominator.

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Step 2.3.1.1

Rewrite $9$ as $3^{2}$ .

$a = \frac{33}{\sqrt{3^{2}}}$

Step 2.3.1.2

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

$a = \frac{33}{3}$

Step 2.3.2

Divide $33$ by $3$ .

$a = 11$