Basic Math Examples

$\frac{\sqrt{98 a^{6} b^{4}}}{\sqrt{2 a^{3} b^{2}}}$

Step 1

Combine $\sqrt{98 a^{6} b^{4}}$ and $\sqrt{2 a^{3} b^{2}}$ into a single radical.

$\sqrt{\frac{98 a^{6} b^{4}}{2 a^{3} b^{2}}}$

Step 2

Reduce the expression $\frac{98 a^{6} b^{4}}{2 a^{3} b^{2}}$ by cancelling the common factors.

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Step 2.1

Factor $2$ out of $98 a^{6} b^{4}$ .

$\sqrt{\frac{2 (49 a^{6} b^{4})}{2 a^{3} b^{2}}}$

Step 2.2

Factor $2$ out of $2 a^{3} b^{2}$ .

$\sqrt{\frac{2 (49 a^{6} b^{4})}{2 (a^{3} b^{2})}}$

Step 2.3

Cancel the common factor.

$\sqrt{\frac{2 (49 a^{6} b^{4})}{2 (a^{3} b^{2})}}$

Step 2.4

Rewrite the expression.

$\sqrt{\frac{49 a^{6} b^{4}}{a^{3} b^{2}}}$

Step 3

Cancel the common factor of $a^{6}$ and $a^{3}$ .

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Step 3.1

Factor $a^{3}$ out of $49 a^{6} b^{4}$ .

$\sqrt{\frac{a^{3} (49 a^{3} b^{4})}{a^{3} b^{2}}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $a^{3}$ out of $a^{3} b^{2}$ .

$\sqrt{\frac{a^{3} (49 a^{3} b^{4})}{a^{3} (b^{2})}}$

Step 3.2.2

Cancel the common factor.

$\sqrt{\frac{a^{3} (49 a^{3} b^{4})}{a^{3} b^{2}}}$

Step 3.2.3

Rewrite the expression.

$\sqrt{\frac{49 a^{3} b^{4}}{b^{2}}}$

Step 4

Cancel the common factor of $b^{4}$ and $b^{2}$ .

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Step 4.1

Factor $b^{2}$ out of $49 a^{3} b^{4}$ .

$\sqrt{\frac{b^{2} (49 a^{3} b^{2})}{b^{2}}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Multiply by $1$ .

$\sqrt{\frac{b^{2} (49 a^{3} b^{2})}{b^{2} \cdot 1}}$

Step 4.2.2

Cancel the common factor.

$\sqrt{\frac{b^{2} (49 a^{3} b^{2})}{b^{2} \cdot 1}}$

Step 4.2.3

Rewrite the expression.

$\sqrt{\frac{49 a^{3} b^{2}}{1}}$

Step 4.2.4

Divide $49 a^{3} b^{2}$ by $1$ .

$\sqrt{49 a^{3} b^{2}}$

Step 5

Rewrite $49 a^{3} b^{2}$ as ${(7 a b)}^{2} a$ .

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Step 5.1

Rewrite $49$ as $7^{2}$ .

$\sqrt{7^{2} a^{3} b^{2}}$

Step 5.2

Factor out $a^{2}$ .

$\sqrt{7^{2} (a^{2} a) b^{2}}$

Step 5.3

Move $a$ .

$\sqrt{7^{2} (a^{2}) b^{2} a}$

Step 5.4

Rewrite $7^{2} (a^{2}) b^{2}$ as ${(7 a b)}^{2}$ .

$\sqrt{{(7 a b)}^{2} a}$

Step 6

Pull terms out from under the radical.

$7 a b \sqrt{a}$