What is the square root of 16/36?
Understand the Problem
The question is asking to calculate the square root of the fraction 16/36. To solve this, first, we simplify the fraction and then find the square root of the resulting value.
Answer
$\frac{2}{3}$
Answer for screen readers
The final answer is $\frac{2}{3}$.
Steps to Solve
- Simplify the fraction
To simplify the fraction $\frac{16}{36}$, we need to find the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 16 and 36 is 4.
So, we divide both the numerator and the denominator by 4:
$$ \frac{16 \div 4}{36 \div 4} = \frac{4}{9} $$
- Calculate the square root
Next, we need to find the square root of the simplified fraction $\frac{4}{9}$. We can find the square root of a fraction by taking the square root of the numerator and the denominator separately.
So:
$$ \sqrt{\frac{4}{9}} = \frac{\sqrt{4}}{\sqrt{9}} = \frac{2}{3} $$
The final answer is $\frac{2}{3}$.
More Information
The square root of a fraction can be found by separately taking the square root of the numerator and the denominator. This is a useful property when dealing with square roots of fractions. Simplifying the fraction first can make calculations easier.
Tips
- Forgetting to simplify the fraction before taking the square root.
- Not knowing that the square root of a fraction can be done by taking the square root of the numerator and denominator separately.
