64/121 Square Root: Understanding Calculation and Exact Solution

The square root of \( \frac{64}{121} \) is a mathematical calculation that involves finding the number which, when multiplied by itself, gives \( \frac{64}{121} \).

Numerical Approximation:

The approximate value of \( \sqrt{\frac{64}{121}} \) is approximately \( 0.533 \).

Exact Calculation:

The exact value of \( \sqrt{\frac{64}{121}} \) can be expressed as \( \frac{8}{11} \).

Step-by-Step Solution:

1. Calculate the square roots of 64 and 121 separately:
   • \( \sqrt{64} = 8 \)
   • \( \sqrt{121} = 11 \)
2. Therefore, \( \sqrt{\frac{64}{121}} = \frac{\sqrt{64}}{\sqrt{121}} = \frac{8}{11} \).

Verification:

Therefore, the square root of \( \frac{64}{121} \) is \( \frac{8}{11} \) or approximately 0.533.

1. Introduction

2. Numerical Approximation

3. Exact Calculation

   • Calculate the square roots of 64 and 121 separately:

   • Express the exact value of \( \sqrt{\frac{64}{121}} \) as \( \frac{8}{11} \).

4. Step-by-Step Solution

   1. Calculate the square roots of 64 and 121 separately:

   2. Therefore, \( \sqrt{\frac{64}{121}} = \frac{\sqrt{64}}{\sqrt{121}} = \frac{8}{11} \).

5. Verification

   Calculated Value:	\( \frac{8}{11} \)
   Numerical Approximation:	0.533 (approximately)

The square root of \( \frac{64}{121} \) is a fundamental mathematical calculation that involves finding the number which, when multiplied by itself, results in \( \frac{64}{121} \). This concept is crucial in mathematics and various fields where precise measurements and calculations are required. Understanding how to compute and interpret the square root of fractions enhances mathematical literacy and problem-solving skills.

The numerical approximation of \( \sqrt{\frac{64}{121}} \) gives us an approximate value that is useful in practical calculations:

The approximate value is approximately \( 0.533 \).

To find the exact value of \( \sqrt{\frac{64}{121}} \), follow these steps:

1. Calculate the square roots of 64 and 121 separately:

   • \( \sqrt{64} = 8 \)

   • \( \sqrt{121} = 11 \)

2. Therefore, \( \sqrt{\frac{64}{121}} = \frac{\sqrt{64}}{\sqrt{121}} = \frac{8}{11} \).

1. Calculate the square roots of 64 and 121 separately:

   • \( \sqrt{64} = 8 \)

   • \( \sqrt{121} = 11 \)

2. Therefore, \( \sqrt{\frac{64}{121}} = \frac{\sqrt{64}}{\sqrt{121}} = \frac{8}{11} \).