Simplify 4/( square root of 2)+2/( square root of 3)

$\frac{4}{\sqrt{2}} + \frac{2}{\sqrt{3}}$

Step 1

Simplify each term.

Multiply $\frac{4}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

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

Combine and simplify the denominator.

Multiply $\frac{4}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$\frac{4 \sqrt{2}}{\sqrt{2} \sqrt{2}} + \frac{2}{\sqrt{3}}$

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

$\frac{4 \sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}} + \frac{2}{\sqrt{3}}$

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

$\frac{4 \sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}} + \frac{2}{\sqrt{3}}$

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

$\frac{4 \sqrt{2}}{{\sqrt{2}}^{1 + 1}} + \frac{2}{\sqrt{3}}$

Add $1$ and $1$ .

$\frac{4 \sqrt{2}}{{\sqrt{2}}^{2}} + \frac{2}{\sqrt{3}}$

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

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

$\frac{4 \sqrt{2}}{{(2^{\frac{1}{2}})}^{2}} + \frac{2}{\sqrt{3}}$

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

$\frac{4 \sqrt{2}}{2^{\frac{1}{2} \cdot 2}} + \frac{2}{\sqrt{3}}$

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

$\frac{4 \sqrt{2}}{2^{\frac{2}{2}}} + \frac{2}{\sqrt{3}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{4 \sqrt{2}}{2^{\frac{2}{2}}} + \frac{2}{\sqrt{3}}$

Rewrite the expression.

$\frac{4 \sqrt{2}}{2^{1}} + \frac{2}{\sqrt{3}}$

Evaluate the exponent.

$\frac{4 \sqrt{2}}{2} + \frac{2}{\sqrt{3}}$

Cancel the common factor of $4$ and $2$ .

Factor $2$ out of $4 \sqrt{2}$ .

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

Cancel the common factors.

Factor $2$ out of $2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

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

Combine and simplify the denominator.

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

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

Raise $\sqrt{3}$ to the power of $1$ .

$2 \sqrt{2} + \frac{2 \sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}}$

Raise $\sqrt{3}$ to the power of $1$ .

$2 \sqrt{2} + \frac{2 \sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}}$

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

$2 \sqrt{2} + \frac{2 \sqrt{3}}{{\sqrt{3}}^{1 + 1}}$

Add $1$ and $1$ .

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

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

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

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

$2 \sqrt{2} + \frac{2 \sqrt{3}}{3^{\frac{1}{2} \cdot 2}}$

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$2 \sqrt{2} + \frac{2 \sqrt{3}}{3^{1}}$

Evaluate the exponent.

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

Step 2

To write $2 \sqrt{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 3

Combine $2 \sqrt{2}$ and $\frac{3}{3}$ .

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

Step 4

Simplify the expression.

Combine the numerators over the common denominator.

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

Multiply $3$ by $2$ .

$\frac{6 \sqrt{2} + 2 \sqrt{3}}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{6 \sqrt{2} + 2 \sqrt{3}}{3}$

Decimal Form:

$3.98312766 \dots$

Simplify 4/( square root of 2)+2/( square root of 3)

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