Algebra Examples

$\sqrt{42 x^{5}} \div \sqrt{6 x^{3}}$

Step 1

Rewrite the division as a fraction.

$\frac{\sqrt{42 x^{5}}}{\sqrt{6 x^{3}}}$

Step 2

Combine $\sqrt{42 x^{5}}$ and $\sqrt{6 x^{3}}$ into a single radical.

$\sqrt{\frac{42 x^{5}}{6 x^{3}}}$

Step 3

Reduce the expression $\frac{42 x^{5}}{6 x^{3}}$ by cancelling the common factors.

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Step 3.1

Factor $6$ out of $42 x^{5}$ .

$\sqrt{\frac{6 (7 x^{5})}{6 x^{3}}}$

Step 3.2

Factor $6$ out of $6 x^{3}$ .

$\sqrt{\frac{6 (7 x^{5})}{6 (x^{3})}}$

Step 3.3

Cancel the common factor.

$\sqrt{\frac{6 (7 x^{5})}{6 x^{3}}}$

Step 3.4

Rewrite the expression.

$\sqrt{\frac{7 x^{5}}{x^{3}}}$

Step 4

Cancel the common factor of $x^{5}$ and $x^{3}$ .

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Step 4.1

Factor $x^{3}$ out of $7 x^{5}$ .

$\sqrt{\frac{x^{3} (7 x^{2})}{x^{3}}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Multiply by $1$ .

$\sqrt{\frac{x^{3} (7 x^{2})}{x^{3} \cdot 1}}$

Step 4.2.2

Cancel the common factor.

$\sqrt{\frac{x^{3} (7 x^{2})}{x^{3} \cdot 1}}$

Step 4.2.3

Rewrite the expression.

$\sqrt{\frac{7 x^{2}}{1}}$

Step 4.2.4

Divide $7 x^{2}$ by $1$ .

$\sqrt{7 x^{2}}$

Step 5

Reorder $7$ and $x^{2}$ .

$\sqrt{x^{2} \cdot 7}$

Step 6

Pull terms out from under the radical.

$x \sqrt{7}$