Simplify ( square root of 50)/9+( square root of 8)/5

$\frac{\sqrt{50}}{9} + \frac{\sqrt{8}}{5}$

Step 1

Simplify each term.

Simplify the numerator.

Rewrite

$50$ as

$5^{2} \cdot 2$ .

Factor

$25$ out of

$50$ .

$\frac{\sqrt{25 (2)}}{9} + \frac{\sqrt{8}}{5}$

Rewrite

$25$ as

$5^{2}$ .

$\frac{\sqrt{5^{2} \cdot 2}}{9} + \frac{\sqrt{8}}{5}$

Pull terms out from under the radical.

$\frac{5 \sqrt{2}}{9} + \frac{\sqrt{8}}{5}$

Simplify the numerator.

Rewrite

$8$ as

$2^{2} \cdot 2$ .

Factor

$4$ out of

$8$ .

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

Rewrite

$4$ as

$2^{2}$ .

$\frac{5 \sqrt{2}}{9} + \frac{\sqrt{2^{2} \cdot 2}}{5}$

Pull terms out from under the radical.

$\frac{5 \sqrt{2}}{9} + \frac{2 \sqrt{2}}{5}$

Step 2

To write

$\frac{5 \sqrt{2}}{9}$ as a fraction with a common denominator, multiply by

$\frac{5}{5}$ .

$\frac{5 \sqrt{2}}{9} \cdot \frac{5}{5} + \frac{2 \sqrt{2}}{5}$

Step 3

To write

$\frac{2 \sqrt{2}}{5}$ as a fraction with a common denominator, multiply by

$\frac{9}{9}$ .

$\frac{5 \sqrt{2}}{9} \cdot \frac{5}{5} + \frac{2 \sqrt{2}}{5} \cdot \frac{9}{9}$

Step 4

Write each expression with a common denominator of

$45$ , by multiplying each by an appropriate factor of

$1$ .

Multiply

$\frac{5 \sqrt{2}}{9}$ by

$\frac{5}{5}$ .

$\frac{5 \sqrt{2} \cdot 5}{9 \cdot 5} + \frac{2 \sqrt{2}}{5} \cdot \frac{9}{9}$

Multiply

$9$ by

$5$ .

$\frac{5 \sqrt{2} \cdot 5}{45} + \frac{2 \sqrt{2}}{5} \cdot \frac{9}{9}$

Multiply

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

$\frac{9}{9}$ .

$\frac{5 \sqrt{2} \cdot 5}{45} + \frac{2 \sqrt{2} \cdot 9}{5 \cdot 9}$

Multiply

$5$ by

$9$ .

$\frac{5 \sqrt{2} \cdot 5}{45} + \frac{2 \sqrt{2} \cdot 9}{45}$

Step 5

Combine the numerators over the common denominator.

$\frac{5 \sqrt{2} \cdot 5 + 2 \sqrt{2} \cdot 9}{45}$

Step 6

Simplify the numerator.

Multiply

$5$ by

$5$ .

$\frac{25 \sqrt{2} + 2 \sqrt{2} \cdot 9}{45}$

Multiply

$9$ by

$2$ .

$\frac{25 \sqrt{2} + 18 \sqrt{2}}{45}$

Add

$25 \sqrt{2}$ and

$18 \sqrt{2}$ .

$\frac{43 \sqrt{2}}{45}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{43 \sqrt{2}}{45}$

Decimal Form:

$1.35135962 \dots$

Simplify ( square root of 50)/9+( square root of 8)/5

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