Simplify 20/(5 square root of 7-2 square root of 5)

$\frac{20}{5 \sqrt{7} - 2 \sqrt{5}}$

Step 1

Multiply $\frac{20}{5 \sqrt{7} - 2 \sqrt{5}}$ by $\frac{5 \sqrt{7} + 2 \sqrt{5}}{5 \sqrt{7} + 2 \sqrt{5}}$ .

$\frac{20}{5 \sqrt{7} - 2 \sqrt{5}} \cdot \frac{5 \sqrt{7} + 2 \sqrt{5}}{5 \sqrt{7} + 2 \sqrt{5}}$

Step 2

Multiply $\frac{20}{5 \sqrt{7} - 2 \sqrt{5}}$ by $\frac{5 \sqrt{7} + 2 \sqrt{5}}{5 \sqrt{7} + 2 \sqrt{5}}$ .

$\frac{20 (5 \sqrt{7} + 2 \sqrt{5})}{(5 \sqrt{7} - 2 \sqrt{5}) (5 \sqrt{7} + 2 \sqrt{5})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{20 (5 \sqrt{7} + 2 \sqrt{5})}{25 {\sqrt{7}}^{2} + 10 \sqrt{35} - 10 \sqrt{35} - 4 {\sqrt{5}}^{2}}$

Step 4

Simplify.

$\frac{20 (5 \sqrt{7} + 2 \sqrt{5})}{155}$

Step 5

Cancel the common factor of $20$ and $155$ .

Factor $5$ out of $20 (5 \sqrt{7} + 2 \sqrt{5})$ .

$\frac{5 (4 (5 \sqrt{7} + 2 \sqrt{5}))}{155}$

Cancel the common factors.

Factor $5$ out of $155$ .

$\frac{5 (4 (5 \sqrt{7} + 2 \sqrt{5}))}{5 (31)}$

Cancel the common factor.

$\frac{5 (4 (5 \sqrt{7} + 2 \sqrt{5}))}{5 \cdot 31}$

Rewrite the expression.

$\frac{4 (5 \sqrt{7} + 2 \sqrt{5})}{31}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{4 (5 \sqrt{7} + 2 \sqrt{5})}{31}$

Decimal Form:

$2.28398613 \dots$