Basic Math Examples

$10 \div \sqrt{90}$

Step 1

Rewrite the division as a fraction.

$\frac{10}{\sqrt{90}}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $90$ as $3^{2} \cdot 10$ .

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Step 2.1.1

Factor $9$ out of $90$ .

$\frac{10}{\sqrt{9 (10)}}$

Step 2.1.2

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

$\frac{10}{\sqrt{3^{2} \cdot 10}}$

Step 2.2

Pull terms out from under the radical.

$\frac{10}{3 \sqrt{10}}$

Step 3

Multiply $\frac{10}{3 \sqrt{10}}$ by $\frac{\sqrt{10}}{\sqrt{10}}$ .

$\frac{10}{3 \sqrt{10}} \cdot \frac{\sqrt{10}}{\sqrt{10}}$

Step 4

Combine and simplify the denominator.

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Step 4.1

Multiply $\frac{10}{3 \sqrt{10}}$ by $\frac{\sqrt{10}}{\sqrt{10}}$ .

$\frac{10 \sqrt{10}}{3 \sqrt{10} \sqrt{10}}$

Step 4.2

Move $\sqrt{10}$ .

$\frac{10 \sqrt{10}}{3 (\sqrt{10} \sqrt{10})}$

Step 4.3

Raise $\sqrt{10}$ to the power of $1$ .

$\frac{10 \sqrt{10}}{3 ({\sqrt{10}}^{1} \sqrt{10})}$

Step 4.4

Raise $\sqrt{10}$ to the power of $1$ .

$\frac{10 \sqrt{10}}{3 ({\sqrt{10}}^{1} {\sqrt{10}}^{1})}$

Step 4.5

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{10 \sqrt{10}}{3 {\sqrt{10}}^{1 + 1}}$

Step 4.6

Add $1$ and $1$ .

$\frac{10 \sqrt{10}}{3 {\sqrt{10}}^{2}}$

Step 4.7

Rewrite ${\sqrt{10}}^{2}$ as $10$ .

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Step 4.7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{10}$ as $10^{\frac{1}{2}}$ .

$\frac{10 \sqrt{10}}{3 {(10^{\frac{1}{2}})}^{2}}$

Step 4.7.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{10 \sqrt{10}}{3 \cdot 10^{\frac{1}{2} \cdot 2}}$

Step 4.7.3

Combine $\frac{1}{2}$ and $2$ .

$\frac{10 \sqrt{10}}{3 \cdot 10^{\frac{2}{2}}}$

Step 4.7.4

Cancel the common factor of $2$ .

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Step 4.7.4.1

Cancel the common factor.

$\frac{10 \sqrt{10}}{3 \cdot 10^{\frac{2}{2}}}$

Step 4.7.4.2

Rewrite the expression.

$\frac{10 \sqrt{10}}{3 \cdot 10^{1}}$

Step 4.7.5

Evaluate the exponent.

$\frac{10 \sqrt{10}}{3 \cdot 10}$

Step 5

Cancel the common factor of $10$ .

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Step 5.1

Cancel the common factor.

$\frac{10 \sqrt{10}}{3 \cdot 10}$

Step 5.2

Rewrite the expression.

$\frac{\sqrt{10}}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{10}}{3}$

Decimal Form:

$1.05409255 \dots$