Algebra Examples

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

Step 1

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

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

Step 2

Combine $\frac{25 r^{2}}{36}$ and $t$ .

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

Step 3

Rewrite $\frac{25 r^{2} t}{36}$ as ${(\frac{5 r}{6})}^{2} t$ .

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Step 3.1

Factor the perfect power ${(5 r)}^{2}$ out of $25 r^{2} t$ .

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

Step 3.2

Factor the perfect power $6^{2}$ out of $36$ .

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

Step 3.3

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

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

Step 4

Pull terms out from under the radical.

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

Step 5

Combine $\frac{5 r}{6}$ and $\sqrt{t}$ .

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