Combine square root of 9/6+10

$\sqrt{\frac{9}{6}} + 10$

Step 1

Simplify each term.

Cancel the common factor of $9$ and $6$ .

Factor $3$ out of $9$ .

$\sqrt{\frac{3 (3)}{6}} + 10$

Cancel the common factors.

Factor $3$ out of $6$ .

$\sqrt{\frac{3 \cdot 3}{3 \cdot 2}} + 10$

Cancel the common factor.

$\sqrt{\frac{3 \cdot 3}{3 \cdot 2}} + 10$

Rewrite the expression.

$\sqrt{\frac{3}{2}} + 10$

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

$\frac{\sqrt{3}}{\sqrt{2}} + 10$

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

$\frac{\sqrt{3}}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} + 10$

Combine and simplify the denominator.

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

$\frac{\sqrt{3} \sqrt{2}}{\sqrt{2} \sqrt{2}} + 10$

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

$\frac{\sqrt{3} \sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}} + 10$

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

$\frac{\sqrt{3} \sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}} + 10$

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

$\frac{\sqrt{3} \sqrt{2}}{{\sqrt{2}}^{1 + 1}} + 10$

Add $1$ and $1$ .

$\frac{\sqrt{3} \sqrt{2}}{{\sqrt{2}}^{2}} + 10$

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

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

$\frac{\sqrt{3} \sqrt{2}}{{(2^{\frac{1}{2}})}^{2}} + 10$

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

$\frac{\sqrt{3} \sqrt{2}}{2^{\frac{1}{2} \cdot 2}} + 10$

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

$\frac{\sqrt{3} \sqrt{2}}{2^{\frac{2}{2}}} + 10$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{\sqrt{3} \sqrt{2}}{2^{\frac{2}{2}}} + 10$

Rewrite the expression.

$\frac{\sqrt{3} \sqrt{2}}{2^{1}} + 10$

Evaluate the exponent.

$\frac{\sqrt{3} \sqrt{2}}{2} + 10$

Simplify the numerator.

Combine using the product rule for radicals.

$\frac{\sqrt{3 \cdot 2}}{2} + 10$

Multiply $3$ by $2$ .

$\frac{\sqrt{6}}{2} + 10$

Step 2

To write $10$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{\sqrt{6}}{2} + 10 \cdot \frac{2}{2}$

Step 3

Combine $10$ and $\frac{2}{2}$ .

$\frac{\sqrt{6}}{2} + \frac{10 \cdot 2}{2}$

Step 4

Simplify the expression.

Combine the numerators over the common denominator.

$\frac{\sqrt{6} + 10 \cdot 2}{2}$

Multiply $10$ by $2$ .

$\frac{\sqrt{6} + 20}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{6} + 20}{2}$

Decimal Form:

$11.22474487 \dots$

Combine square root of 9/6+10

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