Simplify square root of 100/(4x^2)

$\sqrt{\frac{100}{4 x^{2}}}$

Step 1

Reduce the expression $\frac{100}{4 x^{2}}$ by cancelling the common factors.

Factor $4$ out of $100$ .

$\sqrt{\frac{4 \cdot 25}{4 x^{2}}}$

Factor $4$ out of $4 x^{2}$ .

$\sqrt{\frac{4 \cdot 25}{4 (x^{2})}}$

Cancel the common factor.

$\sqrt{\frac{4 \cdot 25}{4 x^{2}}}$

Rewrite the expression.

$\sqrt{\frac{25}{x^{2}}}$

Step 2

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

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

Step 3

Rewrite $\frac{5^{2}}{x^{2}}$ as ${(\frac{5}{x})}^{2}$ .

$\sqrt{{(\frac{5}{x})}^{2}}$

Step 4

Pull terms out from under the radical, assuming positive real numbers.

$\frac{5}{x}$