Basic Math Examples

m \sqrt{k + 1 \div 4}

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

Step 1

Rewrite the division as a fraction.

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

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

Step 2

To write

k

$k$ as a fraction with a common denominator, multiply by

\frac{4}{4}

$\frac{4}{4}$ .

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

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

Step 3

Simplify terms.

Tap for more steps...

Step 3.1

Combine

k

$k$ and

\frac{4}{4}

$\frac{4}{4}$ .

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

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

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

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

Step 4

Move

4

$4$ to the left of

k

$k$ .

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

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

Step 5

Rewrite

\frac{4 k + 1}{4}

$\frac{4 k + 1}{4}$ as

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

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

Tap for more steps...

Step 5.1

Factor the perfect power

1^{2}

$1^{2}$ out of

4 k + 1

$4 k + 1$ .

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

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

Step 5.2

Factor the perfect power

2^{2}

$2^{2}$ out of

4

$4$ .

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

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

Step 5.3

Rearrange the fraction

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

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

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

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

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

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

Step 7

Rewrite using the commutative property of multiplication.

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

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

Step 8

Combine

\frac{1}{2}

$\frac{1}{2}$ and

m

$m$ .

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

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

Step 9

Combine

\frac{m}{2}

$\frac{m}{2}$ and

\sqrt{4 k + 1}

$\sqrt{4 k + 1}$ .

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

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