Basic Math Examples

$\frac{5 \sqrt{2}}{4 \sqrt{3} - 2}$

Step 1

Multiply $\frac{5 \sqrt{2}}{4 \sqrt{3} - 2}$ by $\frac{4 \sqrt{3} + 2}{4 \sqrt{3} + 2}$ .

$\frac{5 \sqrt{2}}{4 \sqrt{3} - 2} \cdot \frac{4 \sqrt{3} + 2}{4 \sqrt{3} + 2}$

Step 2

Multiply $\frac{5 \sqrt{2}}{4 \sqrt{3} - 2}$ by $\frac{4 \sqrt{3} + 2}{4 \sqrt{3} + 2}$ .

$\frac{5 \sqrt{2} (4 \sqrt{3} + 2)}{(4 \sqrt{3} - 2) (4 \sqrt{3} + 2)}$

Step 3

Expand the denominator using the FOIL method.

$\frac{5 \sqrt{2} (4 \sqrt{3} + 2)}{16 {\sqrt{3}}^{2} + 8 \sqrt{3} - 8 \sqrt{3} - 4}$

Step 4

Simplify.

$\frac{5 \sqrt{2} (4 \sqrt{3} + 2)}{44}$

Step 5

Cancel the common factor of $4 \sqrt{3} + 2$ and $44$ .

Tap for more steps...

Step 5.1

Factor $2$ out of $5 \sqrt{2} (4 \sqrt{3} + 2)$ .

$\frac{2 (5 \sqrt{2} (2 \sqrt{3} + 1))}{44}$

Step 5.2

Cancel the common factors.

Tap for more steps...

Step 5.2.1

Factor $2$ out of $44$ .

$\frac{2 (5 \sqrt{2} (2 \sqrt{3} + 1))}{2 (22)}$

Step 5.2.2

Cancel the common factor.

$\frac{2 (5 \sqrt{2} (2 \sqrt{3} + 1))}{2 \cdot 22}$

Step 5.2.3

Rewrite the expression.

$\frac{5 \sqrt{2} (2 \sqrt{3} + 1)}{22}$

Step 6

Group $2 \sqrt{3} + 1$ and $\sqrt{2}$ together.

$\frac{5 ((2 \sqrt{3} + 1) \sqrt{2})}{22}$

Step 7

Apply the distributive property.

$\frac{5 (2 \sqrt{3} \sqrt{2} + 1 \sqrt{2})}{22}$

Step 8

Multiply $2 \sqrt{3} \sqrt{2}$ .

Tap for more steps...

Step 8.1

Combine using the product rule for radicals.

$\frac{5 (2 \sqrt{2 \cdot 3} + 1 \sqrt{2})}{22}$

Step 8.2

Multiply $2$ by $3$ .

$\frac{5 (2 \sqrt{6} + 1 \sqrt{2})}{22}$

Step 9

Multiply $\sqrt{2}$ by $1$ .

$\frac{5 (2 \sqrt{6} + \sqrt{2})}{22}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{5 (2 \sqrt{6} + \sqrt{2})}{22}$

Decimal Form:

$1.43481660 \dots$