What is the square root of 9/49?
Understand the Problem
The question is asking for the square root of the fraction 9/49. The approach involves simplifying the fraction before taking the square root, which can be done by taking the square root of the numerator and the denominator separately.
Answer
The square root of $\frac{9}{49}$ is $\frac{3}{7}$.
Answer for screen readers
The square root of the fraction $\frac{9}{49}$ is $\frac{3}{7}$.
Steps to Solve
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Identify the Fraction We start with the fraction $\frac{9}{49}$.
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Take the Square Root of the Numerator Find the square root of the numerator, which is 9: $$ \sqrt{9} = 3 $$
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Take the Square Root of the Denominator Now, find the square root of the denominator, which is 49: $$ \sqrt{49} = 7 $$
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Combine the Results Now, we can write the square root of the fraction as: $$ \sqrt{\frac{9}{49}} = \frac{\sqrt{9}}{\sqrt{49}} = \frac{3}{7} $$
The square root of the fraction $\frac{9}{49}$ is $\frac{3}{7}$.
More Information
The square root of a fraction can be found by taking the square root of the numerator and the square root of the denominator separately. This principle helps simplify the calculation and is universally applicable to any fraction.
Tips
- Not simplifying the fraction first: Sometimes, people might take the square root of the fraction directly without simplifying, leading to incorrect results. Always break it down into the numerator and denominator.
- Miscalculating square roots: It's essential to remember the correct square roots of common numbers like 9 and 49.
