Basic Math Examples

$\frac{\sqrt{32}}{5} + \frac{\sqrt{18}}{7}$

Step 1

Simplify each term.

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Step 1.1

Simplify the numerator.

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Step 1.1.1

Rewrite $32$ as $4^{2} \cdot 2$ .

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Step 1.1.1.1

Factor $16$ out of $32$ .

$\frac{\sqrt{16 (2)}}{5} + \frac{\sqrt{18}}{7}$

Step 1.1.1.2

Rewrite $16$ as $4^{2}$ .

$\frac{\sqrt{4^{2} \cdot 2}}{5} + \frac{\sqrt{18}}{7}$

Step 1.1.2

Pull terms out from under the radical.

$\frac{4 \sqrt{2}}{5} + \frac{\sqrt{18}}{7}$

Step 1.2

Simplify the numerator.

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Step 1.2.1

Rewrite $18$ as $3^{2} \cdot 2$ .

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Step 1.2.1.1

Factor $9$ out of $18$ .

$\frac{4 \sqrt{2}}{5} + \frac{\sqrt{9 (2)}}{7}$

Step 1.2.1.2

Rewrite $9$ as $3^{2}$ .

$\frac{4 \sqrt{2}}{5} + \frac{\sqrt{3^{2} \cdot 2}}{7}$

Step 1.2.2

Pull terms out from under the radical.

$\frac{4 \sqrt{2}}{5} + \frac{3 \sqrt{2}}{7}$

Step 2

To write $\frac{4 \sqrt{2}}{5}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{4 \sqrt{2}}{5} \cdot \frac{7}{7} + \frac{3 \sqrt{2}}{7}$

Step 3

To write $\frac{3 \sqrt{2}}{7}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{4 \sqrt{2}}{5} \cdot \frac{7}{7} + \frac{3 \sqrt{2}}{7} \cdot \frac{5}{5}$

Step 4

Write each expression with a common denominator of $35$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{4 \sqrt{2}}{5}$ by $\frac{7}{7}$ .

$\frac{4 \sqrt{2} \cdot 7}{5 \cdot 7} + \frac{3 \sqrt{2}}{7} \cdot \frac{5}{5}$

Step 4.2

Multiply $5$ by $7$ .

$\frac{4 \sqrt{2} \cdot 7}{35} + \frac{3 \sqrt{2}}{7} \cdot \frac{5}{5}$

Step 4.3

Multiply $\frac{3 \sqrt{2}}{7}$ by $\frac{5}{5}$ .

$\frac{4 \sqrt{2} \cdot 7}{35} + \frac{3 \sqrt{2} \cdot 5}{7 \cdot 5}$

Step 4.4

Multiply $7$ by $5$ .

$\frac{4 \sqrt{2} \cdot 7}{35} + \frac{3 \sqrt{2} \cdot 5}{35}$

Step 5

Combine the numerators over the common denominator.

$\frac{4 \sqrt{2} \cdot 7 + 3 \sqrt{2} \cdot 5}{35}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $7$ by $4$ .

$\frac{28 \sqrt{2} + 3 \sqrt{2} \cdot 5}{35}$

Step 6.2

Multiply $5$ by $3$ .

$\frac{28 \sqrt{2} + 15 \sqrt{2}}{35}$

Step 6.3

Add $28 \sqrt{2}$ and $15 \sqrt{2}$ .

$\frac{43 \sqrt{2}}{35}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{43 \sqrt{2}}{35}$

Decimal Form:

$1.73746237 \dots$