Simplify the Radical Expression square root of 75/36

$\sqrt{\frac{75}{36}}$

Step 1

Cancel the common factor of $75$ and $36$ .

Factor $3$ out of $75$ .

$\sqrt{\frac{3 (25)}{36}}$

Cancel the common factors.

Factor $3$ out of $36$ .

$\sqrt{\frac{3 \cdot 25}{3 \cdot 12}}$

Cancel the common factor.

$\sqrt{\frac{3 \cdot 25}{3 \cdot 12}}$

Rewrite the expression.

$\sqrt{\frac{25}{12}}$

Step 2

Rewrite $\sqrt{\frac{25}{12}}$ as $\frac{\sqrt{25}}{\sqrt{12}}$ .

$\frac{\sqrt{25}}{\sqrt{12}}$

Step 3

Simplify the numerator.

Rewrite $25$ as $5^{2}$ .

$\frac{\sqrt{5^{2}}}{\sqrt{12}}$

Pull terms out from under the radical.

$\frac{| 5 |}{\sqrt{12}}$

The absolute value is the distance between a number and zero. The distance between $0$ and $5$ is $5$ .

$\frac{5}{\sqrt{12}}$

Step 4

Simplify the denominator.

Rewrite $12$ as $2^{2} \cdot 3$ .

Factor $4$ out of $12$ .

$\frac{5}{\sqrt{4 (3)}}$

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

$\frac{5}{\sqrt{2^{2} \cdot 3}}$

Pull terms out from under the radical.

$\frac{5}{| 2 | \sqrt{3}}$

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

$\frac{5}{2 \sqrt{3}}$

Step 5

Multiply $\frac{5}{2 \sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$\frac{5}{2 \sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}}$

Step 6

Combine and simplify the denominator.

Multiply $\frac{5}{2 \sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$\frac{5 \sqrt{3}}{2 \sqrt{3} \sqrt{3}}$

Move $\sqrt{3}$ .

$\frac{5 \sqrt{3}}{2 (\sqrt{3} \sqrt{3})}$

Raise $\sqrt{3}$ to the power of $1$ .

$\frac{5 \sqrt{3}}{2 ({\sqrt{3}}^{1} \sqrt{3})}$

Raise $\sqrt{3}$ to the power of $1$ .

$\frac{5 \sqrt{3}}{2 ({\sqrt{3}}^{1} {\sqrt{3}}^{1})}$

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

$\frac{5 \sqrt{3}}{2 {\sqrt{3}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{5 \sqrt{3}}{2 {\sqrt{3}}^{2}}$

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$\frac{5 \sqrt{3}}{2 {(3^{\frac{1}{2}})}^{2}}$

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

$\frac{5 \sqrt{3}}{2 \cdot 3^{\frac{1}{2} \cdot 2}}$

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

$\frac{5 \sqrt{3}}{2 \cdot 3^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{5 \sqrt{3}}{2 \cdot 3^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{5 \sqrt{3}}{2 \cdot 3^{1}}$

Evaluate the exponent.

$\frac{5 \sqrt{3}}{2 \cdot 3}$

Step 7

Multiply $2$ by $3$ .

$\frac{5 \sqrt{3}}{6}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{5 \sqrt{3}}{6}$

Decimal Form:

$1.44337567 \dots$

Simplify the Radical Expression square root of 75/36

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