What is the square root of 1/49?
Understand the Problem
The question is asking for the square root of the fraction 1/49. To solve this, we apply the property of square roots which states that the square root of a fraction is equal to the square root of the numerator divided by the square root of the denominator.
Answer
The square root of $\frac{1}{49}$ is $\frac{1}{7}$.
Answer for screen readers
The square root of $\frac{1}{49}$ is $\frac{1}{7}$.
Steps to Solve
- Apply the Square Root Property
According to the property of square roots, we can express the square root of a fraction as follows: $$ \sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}} $$
For our problem, this means: $$ \sqrt{\frac{1}{49}} = \frac{\sqrt{1}}{\sqrt{49}} $$
- Calculate the Square Roots of the Numerator and Denominator
Now we find the square roots of both the numerator and the denominator: $$ \sqrt{1} = 1 $$ $$ \sqrt{49} = 7 $$
- Combine the Square Roots
Now we can substitute the calculated square roots back into our earlier expression: $$ \frac{\sqrt{1}}{\sqrt{49}} = \frac{1}{7} $$
The square root of $\frac{1}{49}$ is $\frac{1}{7}$.
More Information
The square root of a fraction simplifies to the fraction composed of the square roots of the numerator and the denominator. Since 49 is a perfect square, it's straightforward to calculate its square root.
Tips
- Mistaking the Square Root of 49: Sometimes, students may incorrectly think $\sqrt{49}$ is something other than 7. Remember that $49 = 7 \times 7$.
- Forgetting the Property of Square Roots: Ensure to apply the property $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$ correctly.
