Pre-Algebra Examples

$\sqrt{1 - (\frac{11}{100} + \frac{4}{10})}$

Step 1

Cancel the common factor of $4$ and $10$ .

Tap for more steps...

Step 1.1

Factor $2$ out of $4$ .

$\sqrt{1 - (\frac{11}{100} + \frac{2 (2)}{10})}$

Step 1.2

Cancel the common factors.

Tap for more steps...

Step 1.2.1

Factor $2$ out of $10$ .

$\sqrt{1 - (\frac{11}{100} + \frac{2 \cdot 2}{2 \cdot 5})}$

Step 1.2.2

Cancel the common factor.

$\sqrt{1 - (\frac{11}{100} + \frac{2 \cdot 2}{2 \cdot 5})}$

Step 1.2.3

Rewrite the expression.

$\sqrt{1 - (\frac{11}{100} + \frac{2}{5})}$

Step 2

To write $\frac{2}{5}$ as a fraction with a common denominator, multiply by $\frac{20}{20}$ .

$\sqrt{1 - (\frac{11}{100} + \frac{2}{5} \cdot \frac{20}{20})}$

Step 3

Write each expression with a common denominator of $100$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.1

Multiply $\frac{2}{5}$ by $\frac{20}{20}$ .

$\sqrt{1 - (\frac{11}{100} + \frac{2 \cdot 20}{5 \cdot 20})}$

Step 3.2

Multiply $5$ by $20$ .

$\sqrt{1 - (\frac{11}{100} + \frac{2 \cdot 20}{100})}$

Step 4

Combine the numerators over the common denominator.

$\sqrt{1 - \frac{11 + 2 \cdot 20}{100}}$

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

Multiply $2$ by $20$ .

$\sqrt{1 - \frac{11 + 40}{100}}$

Step 5.2

Add $11$ and $40$ .

$\sqrt{1 - \frac{51}{100}}$

Step 6

Write $1$ as a fraction with a common denominator.

$\sqrt{\frac{100}{100} - \frac{51}{100}}$

Step 7

Combine the numerators over the common denominator.

$\sqrt{\frac{100 - 51}{100}}$

Step 8

Subtract $51$ from $100$ .

$\sqrt{\frac{49}{100}}$

Step 9

Rewrite $\sqrt{\frac{49}{100}}$ as $\frac{\sqrt{49}}{\sqrt{100}}$ .

$\frac{\sqrt{49}}{\sqrt{100}}$

Step 10

Simplify the numerator.

Tap for more steps...

Step 10.1

Rewrite $49$ as $7^{2}$ .

$\frac{\sqrt{7^{2}}}{\sqrt{100}}$

Step 10.2

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

$\frac{7}{\sqrt{100}}$

Step 11

Simplify the denominator.

Tap for more steps...

Step 11.1

Rewrite $100$ as $10^{2}$ .

$\frac{7}{\sqrt{10^{2}}}$

Step 11.2

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

$\frac{7}{10}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$\frac{7}{10}$

Decimal Form:

$0.7$