Algebra Examples

\sqrt{\frac{25}{36} r^{2} t}

$\sqrt{\frac{25}{36} r^{2} t}$

Step 1

Combine

\frac{25}{36}

$\frac{25}{36}$ and

r^{2}

$r^{2}$ .

\sqrt{\frac{25 r^{2}}{36} t}

$\sqrt{\frac{25 r^{2}}{36} t}$

Step 2

Combine

\frac{25 r^{2}}{36}

$\frac{25 r^{2}}{36}$ and

t

$t$ .

\sqrt{\frac{25 r^{2} t}{36}}

$\sqrt{\frac{25 r^{2} t}{36}}$

Step 3

Rewrite

\frac{25 r^{2} t}{36}

$\frac{25 r^{2} t}{36}$ as

{(\frac{5 r}{6})}^{2} t

${(\frac{5 r}{6})}^{2} t$ .

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Step 3.1

Factor the perfect power

{(5 r)}^{2}

${(5 r)}^{2}$ out of

25 r^{2} t

$25 r^{2} t$ .

\sqrt{\frac{{(5 r)}^{2} t}{36}}

$\sqrt{\frac{{(5 r)}^{2} t}{36}}$

Step 3.2

Factor the perfect power

6^{2}

$6^{2}$ out of

36

$36$ .

\sqrt{\frac{{(5 r)}^{2} t}{6^{2} \cdot 1}}

$\sqrt{\frac{{(5 r)}^{2} t}{6^{2} \cdot 1}}$

Step 3.3

Rearrange the fraction

\frac{{(5 r)}^{2} t}{6^{2} \cdot 1}

$\frac{{(5 r)}^{2} t}{6^{2} \cdot 1}$ .

\sqrt{{(\frac{5 r}{6})}^{2} t}

$\sqrt{{(\frac{5 r}{6})}^{2} t}$

\sqrt{{(\frac{5 r}{6})}^{2} t}

$\sqrt{{(\frac{5 r}{6})}^{2} t}$

Step 4

Pull terms out from under the radical.

\frac{5 r}{6} \sqrt{t}

$\frac{5 r}{6} \sqrt{t}$

Step 5

Combine

\frac{5 r}{6}

$\frac{5 r}{6}$ and

\sqrt{t}

$\sqrt{t}$ .

\frac{5 r \sqrt{t}}{6}

$\frac{5 r \sqrt{t}}{6}$

⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$