Simplify ( square root of 27)/2+( square root of 75)/7

$\frac{\sqrt{27}}{2} + \frac{\sqrt{75}}{7}$

Step 1

Simplify each term.

Simplify the numerator.

Rewrite

$27$ as

$3^{2} \cdot 3$ .

Factor

$9$ out of

$27$ .

$\frac{\sqrt{9 (3)}}{2} + \frac{\sqrt{75}}{7}$

Rewrite

$9$ as

$3^{2}$ .

$\frac{\sqrt{3^{2} \cdot 3}}{2} + \frac{\sqrt{75}}{7}$

Pull terms out from under the radical.

$\frac{3 \sqrt{3}}{2} + \frac{\sqrt{75}}{7}$

Simplify the numerator.

Rewrite

$75$ as

$5^{2} \cdot 3$ .

Factor

$25$ out of

$75$ .

$\frac{3 \sqrt{3}}{2} + \frac{\sqrt{25 (3)}}{7}$

Rewrite

$25$ as

$5^{2}$ .

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

Pull terms out from under the radical.

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

Step 2

To write

$\frac{3 \sqrt{3}}{2}$ as a fraction with a common denominator, multiply by

$\frac{7}{7}$ .

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

Step 3

To write

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

$\frac{2}{2}$ .

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

Step 4

Write each expression with a common denominator of

$14$ , by multiplying each by an appropriate factor of

$1$ .

Multiply

$\frac{3 \sqrt{3}}{2}$ by

$\frac{7}{7}$ .

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

Multiply

$2$ by

$7$ .

$\frac{3 \sqrt{3} \cdot 7}{14} + \frac{5 \sqrt{3}}{7} \cdot \frac{2}{2}$

Multiply

$\frac{5 \sqrt{3}}{7}$ by

$\frac{2}{2}$ .

$\frac{3 \sqrt{3} \cdot 7}{14} + \frac{5 \sqrt{3} \cdot 2}{7 \cdot 2}$

Multiply

$7$ by

$2$ .

$\frac{3 \sqrt{3} \cdot 7}{14} + \frac{5 \sqrt{3} \cdot 2}{14}$

Step 5

Combine the numerators over the common denominator.

$\frac{3 \sqrt{3} \cdot 7 + 5 \sqrt{3} \cdot 2}{14}$

Step 6

Simplify the numerator.

Multiply

$7$ by

$3$ .

$\frac{21 \sqrt{3} + 5 \sqrt{3} \cdot 2}{14}$

Multiply

$2$ by

$5$ .

$\frac{21 \sqrt{3} + 10 \sqrt{3}}{14}$

Add

$21 \sqrt{3}$ and

$10 \sqrt{3}$ .

$\frac{31 \sqrt{3}}{14}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{31 \sqrt{3}}{14}$

Decimal Form:

$3.83525535 \dots$

Simplify ( square root of 27)/2+( square root of 75)/7

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