Simplify ( square root of 6x^2)÷( square root of 4x)

$\sqrt{6 x^{2}} \div \sqrt{4 x}$

Step 1

Rewrite the division as a fraction.

$\frac{\sqrt{6 x^{2}}}{\sqrt{4 x}}$

Step 2

Combine $\sqrt{6 x^{2}}$ and $\sqrt{4 x}$ into a single radical.

$\sqrt{\frac{6 x^{2}}{4 x}}$

Step 3

Reduce the expression $\frac{6 x^{2}}{4 x}$ by cancelling the common factors.

Factor $2$ out of $6 x^{2}$ .

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

Factor $2$ out of $4 x$ .

$\sqrt{\frac{2 (3 x^{2})}{2 (2 x)}}$

Cancel the common factor.

$\sqrt{\frac{2 (3 x^{2})}{2 (2 x)}}$

Rewrite the expression.

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

Step 4

Cancel the common factor of $x^{2}$ and $x$ .

Factor $x$ out of $3 x^{2}$ .

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

Cancel the common factors.

Factor $x$ out of $2 x$ .

$\sqrt{\frac{x (3 x)}{x \cdot 2}}$

Cancel the common factor.

$\sqrt{\frac{x (3 x)}{x \cdot 2}}$

Rewrite the expression.

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

Step 5

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

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

Step 6

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

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

Step 7

Combine and simplify the denominator.

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

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

Step 8

Simplify the numerator.

Combine using the product rule for radicals.

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

Multiply $2$ by $3$ .

$\frac{\sqrt{6 x}}{2}$

Simplify ( square root of 6x^2)÷( square root of 4x)

Related Questions

Support LCMGCF.com by disabling your adblocker.