Simplify (7 square root of 3)/(5-2 square root of 6)

$\frac{7 \sqrt{3}}{5 - 2 \sqrt{6}}$

Step 1

Multiply $\frac{7 \sqrt{3}}{5 - 2 \sqrt{6}}$ by $\frac{5 + 2 \sqrt{6}}{5 + 2 \sqrt{6}}$ .

$\frac{7 \sqrt{3}}{5 - 2 \sqrt{6}} \cdot \frac{5 + 2 \sqrt{6}}{5 + 2 \sqrt{6}}$

Step 2

Multiply $\frac{7 \sqrt{3}}{5 - 2 \sqrt{6}}$ by $\frac{5 + 2 \sqrt{6}}{5 + 2 \sqrt{6}}$ .

$\frac{7 \sqrt{3} (5 + 2 \sqrt{6})}{(5 - 2 \sqrt{6}) (5 + 2 \sqrt{6})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{7 \sqrt{3} (5 + 2 \sqrt{6})}{25 + 10 \sqrt{6} - 10 \sqrt{6} - 4 {\sqrt{6}}^{2}}$

Step 4

Simplify.

$\frac{7 \sqrt{3} (5 + 2 \sqrt{6})}{1}$

Step 5

Divide $7 \sqrt{3} (5 + 2 \sqrt{6})$ by $1$ .

$7 \sqrt{3} (5 + 2 \sqrt{6})$

Step 6

Apply the distributive property.

$7 \sqrt{3} \cdot 5 + 7 \sqrt{3} (2 \sqrt{6})$

Step 7

Multiply $5$ by $7$ .

$35 \sqrt{3} + 7 \sqrt{3} (2 \sqrt{6})$

Step 8

Multiply $7 \sqrt{3} (2 \sqrt{6})$ .

Multiply $2$ by $7$ .

$35 \sqrt{3} + 14 \sqrt{3} \sqrt{6}$

Combine using the product rule for radicals.

$35 \sqrt{3} + 14 \sqrt{6 \cdot 3}$

Multiply $6$ by $3$ .

$35 \sqrt{3} + 14 \sqrt{18}$

Step 9

Simplify each term.

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

Factor $9$ out of $18$ .

$35 \sqrt{3} + 14 \sqrt{9 (2)}$

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

$35 \sqrt{3} + 14 \sqrt{3^{2} \cdot 2}$

Pull terms out from under the radical.

$35 \sqrt{3} + 14 (3 \sqrt{2})$

Multiply $3$ by $14$ .

$35 \sqrt{3} + 42 \sqrt{2}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$35 \sqrt{3} + 42 \sqrt{2}$

Decimal Form:

$120.01874788 \dots$

Simplify (7 square root of 3)/(5-2 square root of 6)

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