Identify fraction square root: Identify the square root of a fraction. The square root of a fraction can be found by taking the square root of the numerator and the denominator separately.Calculate numerator square root: Calculate the square root of the numerator (11). The square root of 11 cannot be simplified further as it is not a perfect square. Therefore, the square root of 11 remains √11.Calculate denominator square root: Calculate the square root of the denominator (36). The square root of 36 is 6, because 6 * 6 = 36.Write fraction square root: Write the square root of the fraction. The square root of the fraction 11/36 is the square root of 11 divided by the square root of 36, which is √11/6.Check for simplifications: Check for any possible simplifications. Since 11 is a prime number and does not have any square factors, the fraction √11/6 cannot be simplified further.

Precalculus

Operations with rational exponents

Full solution

\sqrt{\frac{11}{36}}

Identify fraction square root: Identify the square root of a fraction. $\newline$ The square root of a fraction can be found by taking the square root of the numerator and the denominator separately.
Calculate numerator square root: Calculate the square root of the numerator $11$ . The square root of $11$ cannot be simplified further as it is not a perfect square. Therefore, the square root of $11$ remains $\sqrt{11}$ .
Calculate denominator square root: Calculate the square root of the denominator ( $36$ ). $\newline$ The square root of $36$ is $6$ , because $6 \times 6 = 36$ .
Write fraction square root: Write the square root of the fraction. $\newline$ The square root of the fraction $\frac{11}{36}$ is the square root of $11$ divided by the square root of $36$ , which is $\sqrt{11}/6$ .
Check for simplifications: Check for any possible simplifications. $\newline$ Since $11$ is a prime number and does not have any square factors, the fraction $\sqrt{11}/6$ cannot be simplified further.