What is the square root of 36/16?
Understand the Problem
The question is asking to calculate the square root of the fraction 36 divided by 16. This involves first simplifying the fraction and then finding the square root of the resulting value.
Answer
$\frac{3}{2}$
Answer for screen readers
The square root of the fraction $\frac{36}{16}$ is $\frac{3}{2}$.
Steps to Solve
- Simplify the Fraction First, we need to simplify the fraction $\frac{36}{16}$. We can divide both the numerator and denominator by their greatest common divisor (GCD), which is 4.
$$ \frac{36 \div 4}{16 \div 4} = \frac{9}{4} $$
- Find the Square Root Next, we find the square root of the simplified fraction $\frac{9}{4}$.
The square root of a fraction can be expressed as the square root of the numerator divided by the square root of the denominator.
$$ \sqrt{\frac{9}{4}} = \frac{\sqrt{9}}{\sqrt{4}} = \frac{3}{2} $$
The square root of the fraction $\frac{36}{16}$ is $\frac{3}{2}$.
More Information
The square root of a fraction allows us to break down the square roots into simpler parts, where the square root of 9 is 3 and the square root of 4 is 2. The result, $\frac{3}{2}$, can also be expressed as 1.5.
Tips
- Forgetting to simplify the fraction before taking the square root. Always simplify first to make calculations easier.
- Incorrectly finding the square roots, such as confusing $\sqrt{9}$ with another value. Ensure you know that $\sqrt{9} = 3$.
