What is the square root of 9/36 as a fraction?
The Correct Answer and Explanation is:
To find the square root of the fraction 936\frac{9}{36}369, we can take the square root of the numerator and the denominator separately.
Step-by-Step Solution:
- Start with the given fraction: 936\frac{9}{36}369
- Find the square root of the numerator (9):
The square root of 9 is 3, because: 9=3\sqrt{9} = 39=3 - Find the square root of the denominator (36):
The square root of 36 is 6, because: 36=6\sqrt{36} = 636=6 - Put the results together: 936=936=36\sqrt{\frac{9}{36}} = \frac{\sqrt{9}}{\sqrt{36}} = \frac{3}{6}369=369=63
- Simplify the fraction:
The fraction 36\frac{3}{6}63 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 3: 36=12\frac{3}{6} = \frac{1}{2}63=21
Final Answer:
The square root of 936\frac{9}{36}369 is 12\frac{1}{2}21.
Explanation:
Taking the square root of a fraction involves finding the square root of both the numerator and the denominator separately. This is based on the property of square roots that:ab=ab\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}ba=ba
So, for the fraction 936\frac{9}{36}369, we first find the square roots of 9 and 36, and then simplify the resulting fraction. This is a straightforward process of using basic square root and simplification rules to arrive at the answer 12\frac{1}{2}21.
