Simplify (5 square root of 7)/8+(4 square root of 6)/7

$\frac{5 \sqrt{7}}{8} + \frac{4 \sqrt{6}}{7}$

Step 1

To write $\frac{5 \sqrt{7}}{8}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{5 \sqrt{7}}{8} \cdot \frac{7}{7} + \frac{4 \sqrt{6}}{7}$

Step 2

To write $\frac{4 \sqrt{6}}{7}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{5 \sqrt{7}}{8} \cdot \frac{7}{7} + \frac{4 \sqrt{6}}{7} \cdot \frac{8}{8}$

Step 3

Write each expression with a common denominator of $56$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5 \sqrt{7}}{8}$ by $\frac{7}{7}$ .

$\frac{5 \sqrt{7} \cdot 7}{8 \cdot 7} + \frac{4 \sqrt{6}}{7} \cdot \frac{8}{8}$

Multiply $8$ by $7$ .

$\frac{5 \sqrt{7} \cdot 7}{56} + \frac{4 \sqrt{6}}{7} \cdot \frac{8}{8}$

Multiply $\frac{4 \sqrt{6}}{7}$ by $\frac{8}{8}$ .

$\frac{5 \sqrt{7} \cdot 7}{56} + \frac{4 \sqrt{6} \cdot 8}{7 \cdot 8}$

Multiply $7$ by $8$ .

$\frac{5 \sqrt{7} \cdot 7}{56} + \frac{4 \sqrt{6} \cdot 8}{56}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 \sqrt{7} \cdot 7 + 4 \sqrt{6} \cdot 8}{56}$

Step 5

Simplify the numerator.

Multiply $7$ by $5$ .

$\frac{35 \sqrt{7} + 4 \sqrt{6} \cdot 8}{56}$

Multiply $8$ by $4$ .

$\frac{35 \sqrt{7} + 32 \sqrt{6}}{56}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{35 \sqrt{7} + 32 \sqrt{6}}{56}$

Decimal Form:

$3.05330299 \dots$