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:
$ \frac{\sqrt{1521}}{\sqrt{1849}} = \frac{39}{43} $This result matches option 2.
Similar Questions
- Given that $7^{0.07} = x$, $7^{0.07} = y$ and $x^z = y^3$, then the value of z is close to:
- Find the value of $57^{-8} \div 57^{17} \times 57^{-18}$.
- If $\sqrt{45} + \sqrt{125} = 17.89$, then what will be the value of $\sqrt{180} + \sqrt{80}$?
(Give your answer to one decimal place.) - What is the value of $\frac{4+\sqrt{2}}{\sqrt{2}+1}$?
If $\sqrt{2916} = 54$ then what is the value of the following?
$\sqrt{29.16} + \sqrt{0.2916} + \sqrt{0.002916} + \sqrt{0.00002916}$
- Find the value of $95^{-17} \div 95^{9} \times 95^{-15}$.
- $(\sqrt{5} + \sqrt{11})(\sqrt{5} - \sqrt{11})$ is equal to:
- What is the value of $\sqrt{75} + \sqrt{147}$?
If $\frac{2\sqrt{2}+\sqrt{7}}{2\sqrt{2}-\sqrt{7}} = x + y\sqrt{14}$, find the value of y.
- If $x = 7 + 4\sqrt{3}$, then find the value of $\sqrt{x} + \frac{1}{\sqrt{x}}$
Important Questions from Surds and Indices
Find the cube root of 78402752
Find the value of :
[(3 × 3 × 3 × 3 × 3 × 3) 6 ÷ (3 × 3 × 3 × 3) 7 × 3 4]
The cube root of - 64 × - 1331 is:
If (27) m = (81) n, then m 2: mn = ?
if 49 n + 49 n + 49 n + 49 n + 49 n + 49 n + 49 n = 7 2221 , then n = ?
