Basic Math Examples

\sqrt{\frac{10}{25}}

$\sqrt{\frac{10}{25}}$

Step 1

Cancel the common factor of

10

$10$ and

25

$25$ .

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Step 1.1

Factor

5

$5$ out of

10

$10$ .

\sqrt{\frac{5 (2)}{25}}

$\sqrt{\frac{5 (2)}{25}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor

5

$5$ out of

25

$25$ .

\sqrt{\frac{5 \cdot 2}{5 \cdot 5}}

$\sqrt{\frac{5 \cdot 2}{5 \cdot 5}}$

Step 1.2.2

Cancel the common factor.

$\sqrt{\frac{5 \cdot 2}{5 \cdot 5}}$

Step 1.2.3

Rewrite the expression.

$\sqrt{\frac{2}{5}}$

Step 2

Rewrite

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

$\frac{\sqrt{2}}{\sqrt{5}}$ .

$\frac{\sqrt{2}}{\sqrt{5}}$

Step 3

Multiply

$\frac{\sqrt{2}}{\sqrt{5}}$ by

$\frac{\sqrt{5}}{\sqrt{5}}$ .

$\frac{\sqrt{2}}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}}$

Step 4

Combine and simplify the denominator.

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Step 4.1

Multiply

$\frac{\sqrt{2}}{\sqrt{5}}$ by

$\frac{\sqrt{5}}{\sqrt{5}}$ .

$\frac{\sqrt{2} \sqrt{5}}{\sqrt{5} \sqrt{5}}$

Step 4.2

Raise

$\sqrt{5}$ to the power of

$1$ .

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

Step 4.3

Raise

$\sqrt{5}$ to the power of

$1$ .

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

Step 4.4

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{\sqrt{2} \sqrt{5}}{{\sqrt{5}}^{1 + 1}}$

Step 4.5

Add

$1$ and

$1$ .

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

Step 4.6

Rewrite

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

$5$ .

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Step 4.6.1

Use

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

$\sqrt{5}$ as

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

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

Step 4.6.2

Apply the power rule and multiply exponents,

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

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

Step 4.6.3

Combine

$\frac{1}{2}$ and

$2$ .

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

Step 4.6.4

Cancel the common factor of

$2$ .

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Step 4.6.4.1

Cancel the common factor.

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

Step 4.6.4.2

Rewrite the expression.

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

Step 4.6.5

Evaluate the exponent.

$\frac{\sqrt{2} \sqrt{5}}{5}$

Step 5

Simplify the numerator.

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Step 5.1

Combine using the product rule for radicals.

$\frac{\sqrt{2 \cdot 5}}{5}$

Step 5.2

Multiply

$2$ by

$5$ .

$\frac{\sqrt{10}}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{10}}{5}$

Decimal Form:

$0.63245553 \dots$