Basic Math Examples

$\sqrt{\frac{2}{100} \cdot {(1)}^{2}} \cdot {(\frac{12}{15})}^{2}$

Step 1

Combine $\frac{2}{100}$ and $1^{2}$ .

$\sqrt{\frac{2 \cdot 1^{2}}{100}} \cdot {(\frac{12}{15})}^{2}$

Step 2

Reduce the expression $\frac{2 \cdot 1^{2}}{100}$ by cancelling the common factors.

Tap for more steps...

Step 2.1

Factor $2$ out of $2 \cdot 1^{2}$ .

$\sqrt{\frac{2 (1^{2})}{100}} \cdot {(\frac{12}{15})}^{2}$

Step 2.2

Factor $2$ out of $100$ .

$\sqrt{\frac{2 \cdot 1^{2}}{2 \cdot 50}} \cdot {(\frac{12}{15})}^{2}$

Step 2.3

Cancel the common factor.

$\sqrt{\frac{2 \cdot 1^{2}}{2 \cdot 50}} \cdot {(\frac{12}{15})}^{2}$

Step 2.4

Rewrite the expression.

$\sqrt{\frac{1^{2}}{50}} \cdot {(\frac{12}{15})}^{2}$

Step 3

One to any power is one.

$\sqrt{\frac{1}{50}} \cdot {(\frac{12}{15})}^{2}$

Step 4

Rewrite $\sqrt{\frac{1}{50}}$ as $\frac{\sqrt{1}}{\sqrt{50}}$ .

$\frac{\sqrt{1}}{\sqrt{50}} \cdot {(\frac{12}{15})}^{2}$

Step 5

Any root of $1$ is $1$ .

$\frac{1}{\sqrt{50}} \cdot {(\frac{12}{15})}^{2}$

Step 6

Simplify the denominator.

Tap for more steps...

Step 6.1

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

Tap for more steps...

Step 6.1.1

Factor $25$ out of $50$ .

$\frac{1}{\sqrt{25 (2)}} \cdot {(\frac{12}{15})}^{2}$

Step 6.1.2

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

$\frac{1}{\sqrt{5^{2} \cdot 2}} \cdot {(\frac{12}{15})}^{2}$

Step 6.2

Pull terms out from under the radical.

$\frac{1}{5 \sqrt{2}} \cdot {(\frac{12}{15})}^{2}$

Step 7

Multiply $\frac{1}{5 \sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$\frac{1}{5 \sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} \cdot {(\frac{12}{15})}^{2}$

Step 8

Combine and simplify the denominator.

Tap for more steps...

Step 8.1

Multiply $\frac{1}{5 \sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$\frac{\sqrt{2}}{5 \sqrt{2} \sqrt{2}} \cdot {(\frac{12}{15})}^{2}$

Step 8.2

Move $\sqrt{2}$ .

$\frac{\sqrt{2}}{5 (\sqrt{2} \sqrt{2})} \cdot {(\frac{12}{15})}^{2}$

Step 8.3

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

$\frac{\sqrt{2}}{5 ({\sqrt{2}}^{1} \sqrt{2})} \cdot {(\frac{12}{15})}^{2}$

Step 8.4

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

$\frac{\sqrt{2}}{5 ({\sqrt{2}}^{1} {\sqrt{2}}^{1})} \cdot {(\frac{12}{15})}^{2}$

Step 8.5

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

$\frac{\sqrt{2}}{5 {\sqrt{2}}^{1 + 1}} \cdot {(\frac{12}{15})}^{2}$

Step 8.6

Add $1$ and $1$ .

$\frac{\sqrt{2}}{5 {\sqrt{2}}^{2}} \cdot {(\frac{12}{15})}^{2}$

Step 8.7

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

Tap for more steps...

Step 8.7.1

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

$\frac{\sqrt{2}}{5 {(2^{\frac{1}{2}})}^{2}} \cdot {(\frac{12}{15})}^{2}$

Step 8.7.2

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

$\frac{\sqrt{2}}{5 \cdot 2^{\frac{1}{2} \cdot 2}} \cdot {(\frac{12}{15})}^{2}$

Step 8.7.3

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

$\frac{\sqrt{2}}{5 \cdot 2^{\frac{2}{2}}} \cdot {(\frac{12}{15})}^{2}$

Step 8.7.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 8.7.4.1

Cancel the common factor.

$\frac{\sqrt{2}}{5 \cdot 2^{\frac{2}{2}}} \cdot {(\frac{12}{15})}^{2}$

Step 8.7.4.2

Rewrite the expression.

$\frac{\sqrt{2}}{5 \cdot 2^{1}} \cdot {(\frac{12}{15})}^{2}$

Step 8.7.5

Evaluate the exponent.

$\frac{\sqrt{2}}{5 \cdot 2} \cdot {(\frac{12}{15})}^{2}$

Step 9

Multiply $5$ by $2$ .

$\frac{\sqrt{2}}{10} \cdot {(\frac{12}{15})}^{2}$

Step 10

Cancel the common factor of $12$ and $15$ .

Tap for more steps...

Step 10.1

Factor $3$ out of $12$ .

$\frac{\sqrt{2}}{10} \cdot {(\frac{3 (4)}{15})}^{2}$

Step 10.2

Cancel the common factors.

Tap for more steps...

Step 10.2.1

Factor $3$ out of $15$ .

$\frac{\sqrt{2}}{10} \cdot {(\frac{3 \cdot 4}{3 \cdot 5})}^{2}$

Step 10.2.2

Cancel the common factor.

$\frac{\sqrt{2}}{10} \cdot {(\frac{3 \cdot 4}{3 \cdot 5})}^{2}$

Step 10.2.3

Rewrite the expression.

$\frac{\sqrt{2}}{10} \cdot {(\frac{4}{5})}^{2}$

Step 11

Apply the product rule to $\frac{4}{5}$ .

$\frac{\sqrt{2}}{10} \cdot \frac{4^{2}}{5^{2}}$

Step 12

Combine.

$\frac{\sqrt{2} \cdot 4^{2}}{10 \cdot 5^{2}}$

Step 13

Simplify the expression.

Tap for more steps...

Step 13.1

Raise $4$ to the power of $2$ .

$\frac{\sqrt{2} \cdot 16}{10 \cdot 5^{2}}$

Step 13.2

Raise $5$ to the power of $2$ .

$\frac{\sqrt{2} \cdot 16}{10 \cdot 25}$

Step 13.3

Move $16$ to the left of $\sqrt{2}$ .

$\frac{16 \sqrt{2}}{10 \cdot 25}$

Step 13.4

Multiply $10$ by $25$ .

$\frac{16 \sqrt{2}}{250}$

Step 14

Cancel the common factor of $16$ and $250$ .

Tap for more steps...

Step 14.1

Factor $2$ out of $16 \sqrt{2}$ .

$\frac{2 (8 \sqrt{2})}{250}$

Step 14.2

Cancel the common factors.

Tap for more steps...

Step 14.2.1

Factor $2$ out of $250$ .

$\frac{2 (8 \sqrt{2})}{2 (125)}$

Step 14.2.2

Cancel the common factor.

$\frac{2 (8 \sqrt{2})}{2 \cdot 125}$

Step 14.2.3

Rewrite the expression.

$\frac{8 \sqrt{2}}{125}$

Step 15

The result can be shown in multiple forms.

Exact Form:

$\frac{8 \sqrt{2}}{125}$

Decimal Form:

$0.09050966 \dots$