Simplify (2 square root of 2)/( square root of 3- square root of 2)

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

Step 1

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

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

Step 2

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

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

Step 3

Expand the denominator using the FOIL method.

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

Step 4

Simplify.

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

Step 5

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

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

Step 6

Apply the distributive property.

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

Step 7

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

Combine using the product rule for radicals.

$2 \sqrt{3 \cdot 2} + 2 \sqrt{2} \sqrt{2}$

Multiply $3$ by $2$ .

$2 \sqrt{6} + 2 \sqrt{2} \sqrt{2}$

Step 8

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

Raise $\sqrt{2}$ to the power of $1$ .

$2 \sqrt{6} + 2 ({\sqrt{2}}^{1} \sqrt{2})$

Raise $\sqrt{2}$ to the power of $1$ .

$2 \sqrt{6} + 2 ({\sqrt{2}}^{1} {\sqrt{2}}^{1})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 \sqrt{6} + 2 {\sqrt{2}}^{1 + 1}$

Add $1$ and $1$ .

$2 \sqrt{6} + 2 {\sqrt{2}}^{2}$

Step 9

Simplify each term.

Rewrite ${\sqrt{2}}^{2}$ as $2$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

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

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$2 \sqrt{6} + 2 \cdot 2^{\frac{1}{2} \cdot 2}$

Combine $\frac{1}{2}$ and $2$ .

$2 \sqrt{6} + 2 \cdot 2^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \sqrt{6} + 2 \cdot 2^{\frac{2}{2}}$

Rewrite the expression.

$2 \sqrt{6} + 2 \cdot 2^{1}$

Evaluate the exponent.

$2 \sqrt{6} + 2 \cdot 2$

Multiply $2$ by $2$ .

$2 \sqrt{6} + 4$

Step 10

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{6} + 4$

Decimal Form:

$8.89897948 \dots$

Simplify (2 square root of 2)/( square root of 3- square root of 2)

Related Questions

Support LCMGCF.com by disabling your adblocker.