QuestionSimplify. $\sqrt{\frac{15}{135}}$

Studdy Solution

STEP 1

1. We are asked to simplify the square root of a fraction.
2. The fraction inside the square root can be simplified before taking the square root.
3. Simplifying the fraction will make it easier to compute the square root.

STEP 2

1. Simplify the fraction $\frac{15}{135}$ .
2. Compute the square root of the simplified fraction.

STEP 3

Simplify the fraction $\frac{15}{135}$ by finding the greatest common divisor (GCD) of the numerator and the denominator.
The GCD of 15 and 135 is 15.
$\frac{15}{135} = \frac{15 \div 15}{135 \div 15} = \frac{1}{9}$

STEP 4

Compute the square root of the simplified fraction $\frac{1}{9}$ .
$\sqrt{\frac{1}{9}} = \frac{\sqrt{1}}{\sqrt{9}} = \frac{1}{3}$
The simplified form of the expression is:
$\boxed{\frac{1}{3}}$

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