Finding the Square Root of a Fraction

The problem requires finding the square root of the fraction $\frac{1521}{1849}$. This can be calculated by finding the square root of the numerator and the denominator separately.

The expression is: $ \sqrt{\frac{1521}{1849}} $ This is equivalent to: $ \frac{\sqrt{1521}}{\sqrt{1849}} $

Calculating Numerator Square Root

We need to find the value of $\sqrt{1521}$.

• Estimate: $30^2 = 900$ and $40^2 = 1600$. The square root must be between 30 and 40.
• Check the last digit: The number 1521 ends in 1. Its square root must end in 1 or 9.
• Possible roots are 31 and 39.
• Test 39: $39 \times 39 = 1521$.

Therefore, $\sqrt{1521} = 39$.

Calculating Denominator Square Root

We need to find the value of $\sqrt{1849}$.

• Estimate: $40^2 = 1600$ and $50^2 = 2500$. The square root must be between 40 and 50.
• Check the last digit: The number 1849 ends in 9. Its square root must end in 3 or 7.
• Possible roots are 43 and 47.
• Test 43: $43 \times 43 = 1849$.

Therefore, $\sqrt{1849} = 43$.

Final Calculation

Now, substitute the calculated square roots back into the fraction:

This result matches option 2.