Algebra Examples

$\frac{1}{3} \sqrt{0.36} + \frac{1}{5} \sqrt{900}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $0.36$ as ${0.6}^{2}$ .

$\frac{1}{3} \cdot \sqrt{{0.6}^{2}} + \frac{1}{5} \cdot \sqrt{900}$

Step 1.2

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

$\frac{1}{3} \cdot 0.6 + \frac{1}{5} \cdot \sqrt{900}$

Step 1.3

Cancel the common factor of $0.6$ .

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Step 1.3.1

Factor $0.6$ out of $3$ .

$\frac{1}{0.6 (5)} \cdot 0.6 + \frac{1}{5} \cdot \sqrt{900}$

Step 1.3.2

Cancel the common factor.

$\frac{1}{0.6 \cdot 5} \cdot 0.6 + \frac{1}{5} \cdot \sqrt{900}$

Step 1.3.3

Rewrite the expression.

$\frac{1}{5} + \frac{1}{5} \cdot \sqrt{900}$

Step 1.4

Rewrite $900$ as $30^{2}$ .

$\frac{1}{5} + \frac{1}{5} \cdot \sqrt{30^{2}}$

Step 1.5

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

$\frac{1}{5} + \frac{1}{5} \cdot 30$

Step 1.6

Cancel the common factor of $5$ .

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Step 1.6.1

Factor $5$ out of $30$ .

$\frac{1}{5} + \frac{1}{5} \cdot (5 (6))$

Step 1.6.2

Cancel the common factor.

$\frac{1}{5} + \frac{1}{5} \cdot (5 \cdot 6)$

Step 1.6.3

Rewrite the expression.

$\frac{1}{5} + 6$

Step 2

To write $6$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{1}{5} + 6 \cdot \frac{5}{5}$

Step 3

Combine $6$ and $\frac{5}{5}$ .

$\frac{1}{5} + \frac{6 \cdot 5}{5}$

Step 4

Combine the numerators over the common denominator.

$\frac{1 + 6 \cdot 5}{5}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $6$ by $5$ .

$\frac{1 + 30}{5}$

Step 5.2

Add $1$ and $30$ .

$\frac{31}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{31}{5}$

Decimal Form:

$6.2$

Mixed Number Form:

$6 \frac{1}{5}$