Basic Math Examples

$m \sqrt{k + 1 \div 4}$

Step 1

Rewrite the division as a fraction.

$m \sqrt{k + \frac{1}{4}}$

Step 2

To write $k$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$m \sqrt{k \cdot \frac{4}{4} + \frac{1}{4}}$

Step 3

Simplify terms.

Tap for more steps...

Step 3.1

Combine $k$ and $\frac{4}{4}$ .

$m \sqrt{\frac{k \cdot 4}{4} + \frac{1}{4}}$

Step 3.2

Combine the numerators over the common denominator.

$m \sqrt{\frac{k \cdot 4 + 1}{4}}$

Step 4

Move $4$ to the left of $k$ .

$m \sqrt{\frac{4 k + 1}{4}}$

Step 5

Rewrite $\frac{4 k + 1}{4}$ as ${(\frac{1}{2})}^{2} (4 k + 1)$ .

Tap for more steps...

Step 5.1

Factor the perfect power $1^{2}$ out of $4 k + 1$ .

$m \sqrt{\frac{1^{2} (4 k + 1)}{4}}$

Step 5.2

Factor the perfect power $2^{2}$ out of $4$ .

$m \sqrt{\frac{1^{2} (4 k + 1)}{2^{2} \cdot 1}}$

Step 5.3

Rearrange the fraction $\frac{1^{2} (4 k + 1)}{2^{2} \cdot 1}$ .

$m \sqrt{{(\frac{1}{2})}^{2} (4 k + 1)}$

Step 6

Pull terms out from under the radical.

$m (\frac{1}{2} \sqrt{4 k + 1})$

Step 7

Rewrite using the commutative property of multiplication.

$\frac{1}{2} m \sqrt{4 k + 1}$

Step 8

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

$\frac{m}{2} \sqrt{4 k + 1}$

Step 9

Combine $\frac{m}{2}$ and $\sqrt{4 k + 1}$ .

$\frac{m \sqrt{4 k + 1}}{2}$