Basic Math Examples

$\frac{\sqrt{210}}{\sqrt{500}}$

Step 1

Combine $\sqrt{210}$ and $\sqrt{500}$ into a single radical.

$\sqrt{\frac{210}{500}}$

Step 2

Cancel the common factor of $210$ and $500$ .

Tap for more steps...

Step 2.1

Factor $10$ out of $210$ .

$\sqrt{\frac{10 (21)}{500}}$

Step 2.2

Cancel the common factors.

Tap for more steps...

Step 2.2.1

Factor $10$ out of $500$ .

$\sqrt{\frac{10 \cdot 21}{10 \cdot 50}}$

Step 2.2.2

Cancel the common factor.

$\sqrt{\frac{10 \cdot 21}{10 \cdot 50}}$

Step 2.2.3

Rewrite the expression.

$\sqrt{\frac{21}{50}}$

Step 3

Rewrite $\sqrt{\frac{21}{50}}$ as $\frac{\sqrt{21}}{\sqrt{50}}$ .

$\frac{\sqrt{21}}{\sqrt{50}}$

Step 4

Simplify the denominator.

Tap for more steps...

Step 4.1

Rewrite $50$ as $5^{2} \cdot 2$ .

Tap for more steps...

Step 4.1.1

Factor $25$ out of $50$ .

$\frac{\sqrt{21}}{\sqrt{25 (2)}}$

Step 4.1.2

Rewrite $25$ as $5^{2}$ .

$\frac{\sqrt{21}}{\sqrt{5^{2} \cdot 2}}$

Step 4.2

Pull terms out from under the radical.

$\frac{\sqrt{21}}{5 \sqrt{2}}$

Step 5

Multiply $\frac{\sqrt{21}}{5 \sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$\frac{\sqrt{21}}{5 \sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}$

Step 6

Combine and simplify the denominator.

Tap for more steps...

Step 6.1

Multiply $\frac{\sqrt{21}}{5 \sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$\frac{\sqrt{21} \sqrt{2}}{5 \sqrt{2} \sqrt{2}}$

Step 6.2

Move $\sqrt{2}$ .

$\frac{\sqrt{21} \sqrt{2}}{5 (\sqrt{2} \sqrt{2})}$

Step 6.3

Raise $\sqrt{2}$ to the power of $1$ .

$\frac{\sqrt{21} \sqrt{2}}{5 ({\sqrt{2}}^{1} \sqrt{2})}$

Step 6.4

Raise $\sqrt{2}$ to the power of $1$ .

$\frac{\sqrt{21} \sqrt{2}}{5 ({\sqrt{2}}^{1} {\sqrt{2}}^{1})}$

Step 6.5

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

$\frac{\sqrt{21} \sqrt{2}}{5 {\sqrt{2}}^{1 + 1}}$

Step 6.6

Add $1$ and $1$ .

$\frac{\sqrt{21} \sqrt{2}}{5 {\sqrt{2}}^{2}}$

Step 6.7

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

Tap for more steps...

Step 6.7.1

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

$\frac{\sqrt{21} \sqrt{2}}{5 {(2^{\frac{1}{2}})}^{2}}$

Step 6.7.2

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

$\frac{\sqrt{21} \sqrt{2}}{5 \cdot 2^{\frac{1}{2} \cdot 2}}$

Step 6.7.3

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

$\frac{\sqrt{21} \sqrt{2}}{5 \cdot 2^{\frac{2}{2}}}$

Step 6.7.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 6.7.4.1

Cancel the common factor.

$\frac{\sqrt{21} \sqrt{2}}{5 \cdot 2^{\frac{2}{2}}}$

Step 6.7.4.2

Rewrite the expression.

$\frac{\sqrt{21} \sqrt{2}}{5 \cdot 2^{1}}$

Step 6.7.5

Evaluate the exponent.

$\frac{\sqrt{21} \sqrt{2}}{5 \cdot 2}$

Step 7

Simplify the numerator.

Tap for more steps...

Step 7.1

Combine using the product rule for radicals.

$\frac{\sqrt{21 \cdot 2}}{5 \cdot 2}$

Step 7.2

Multiply $21$ by $2$ .

$\frac{\sqrt{42}}{5 \cdot 2}$

Step 8

Multiply $5$ by $2$ .

$\frac{\sqrt{42}}{10}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{42}}{10}$

Decimal Form:

$0.64807406 \dots$