Basic Math Examples

$4 \sqrt{98} \div \sqrt{48}$

Step 1

Rewrite the division as a fraction.

$\frac{4 \sqrt{98}}{\sqrt{48}}$

Step 2

Combine $\sqrt{98}$ and $\sqrt{48}$ into a single radical.

$4 \sqrt{\frac{98}{48}}$

Step 3

Cancel the common factor of $98$ and $48$ .

Tap for more steps...

Step 3.1

Factor $2$ out of $98$ .

$4 \sqrt{\frac{2 (49)}{48}}$

Step 3.2

Cancel the common factors.

Tap for more steps...

Step 3.2.1

Factor $2$ out of $48$ .

$4 \sqrt{\frac{2 \cdot 49}{2 \cdot 24}}$

Step 3.2.2

Cancel the common factor.

$4 \sqrt{\frac{2 \cdot 49}{2 \cdot 24}}$

Step 3.2.3

Rewrite the expression.

$4 \sqrt{\frac{49}{24}}$

Step 4

Rewrite $\sqrt{\frac{49}{24}}$ as $\frac{\sqrt{49}}{\sqrt{24}}$ .

$4 \frac{\sqrt{49}}{\sqrt{24}}$

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

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

$4 \frac{\sqrt{7^{2}}}{\sqrt{24}}$

Step 5.2

Pull terms out from under the radical, assuming positive real numbers.

$4 \frac{7}{\sqrt{24}}$

Step 6

Simplify the denominator.

Tap for more steps...

Step 6.1

Rewrite $24$ as $2^{2} \cdot 6$ .

Tap for more steps...

Step 6.1.1

Factor $4$ out of $24$ .

$4 \frac{7}{\sqrt{4 (6)}}$

Step 6.1.2

Rewrite $4$ as $2^{2}$ .

$4 \frac{7}{\sqrt{2^{2} \cdot 6}}$

Step 6.2

Pull terms out from under the radical.

$4 \frac{7}{2 \sqrt{6}}$

Step 7

Simplify terms.

Tap for more steps...

Step 7.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 7.1.1

Factor $2$ out of $4$ .

$2 (2) \frac{7}{2 \sqrt{6}}$

Step 7.1.2

Factor $2$ out of $2 \sqrt{6}$ .

$2 (2) \frac{7}{2 (\sqrt{6})}$

Step 7.1.3

Cancel the common factor.

$2 \cdot 2 \frac{7}{2 \sqrt{6}}$

Step 7.1.4

Rewrite the expression.

$2 \frac{7}{\sqrt{6}}$

Step 7.2

Combine $2$ and $\frac{7}{\sqrt{6}}$ .

$\frac{2 \cdot 7}{\sqrt{6}}$

Step 7.3

Multiply $2$ by $7$ .

$\frac{14}{\sqrt{6}}$

Step 8

Multiply $\frac{14}{\sqrt{6}}$ by $\frac{\sqrt{6}}{\sqrt{6}}$ .

$\frac{14}{\sqrt{6}} \cdot \frac{\sqrt{6}}{\sqrt{6}}$

Step 9

Combine and simplify the denominator.

Tap for more steps...

Step 9.1

Multiply $\frac{14}{\sqrt{6}}$ by $\frac{\sqrt{6}}{\sqrt{6}}$ .

$\frac{14 \sqrt{6}}{\sqrt{6} \sqrt{6}}$

Step 9.2

Raise $\sqrt{6}$ to the power of $1$ .

$\frac{14 \sqrt{6}}{{\sqrt{6}}^{1} \sqrt{6}}$

Step 9.3

Raise $\sqrt{6}$ to the power of $1$ .

$\frac{14 \sqrt{6}}{{\sqrt{6}}^{1} {\sqrt{6}}^{1}}$

Step 9.4

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

$\frac{14 \sqrt{6}}{{\sqrt{6}}^{1 + 1}}$

Step 9.5

Add $1$ and $1$ .

$\frac{14 \sqrt{6}}{{\sqrt{6}}^{2}}$

Step 9.6

Rewrite ${\sqrt{6}}^{2}$ as $6$ .

Tap for more steps...

Step 9.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6}$ as $6^{\frac{1}{2}}$ .

$\frac{14 \sqrt{6}}{{(6^{\frac{1}{2}})}^{2}}$

Step 9.6.2

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

$\frac{14 \sqrt{6}}{6^{\frac{1}{2} \cdot 2}}$

Step 9.6.3

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

$\frac{14 \sqrt{6}}{6^{\frac{2}{2}}}$

Step 9.6.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 9.6.4.1

Cancel the common factor.

$\frac{14 \sqrt{6}}{6^{\frac{2}{2}}}$

Step 9.6.4.2

Rewrite the expression.

$\frac{14 \sqrt{6}}{6^{1}}$

Step 9.6.5

Evaluate the exponent.

$\frac{14 \sqrt{6}}{6}$

Step 10

Cancel the common factor of $14$ and $6$ .

Tap for more steps...

Step 10.1

Factor $2$ out of $14 \sqrt{6}$ .

$\frac{2 (7 \sqrt{6})}{6}$

Step 10.2

Cancel the common factors.

Tap for more steps...

Step 10.2.1

Factor $2$ out of $6$ .

$\frac{2 (7 \sqrt{6})}{2 (3)}$

Step 10.2.2

Cancel the common factor.

$\frac{2 (7 \sqrt{6})}{2 \cdot 3}$

Step 10.2.3

Rewrite the expression.

$\frac{7 \sqrt{6}}{3}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\frac{7 \sqrt{6}}{3}$

Decimal Form:

$5.71547606 \dots$