Square Root of 64/121: Calculation and Explanation

To find the square root of \( \frac{64}{121} \), follow these steps:

1. Calculate the square root of the numerator and the denominator separately:

Square root of 64:	\( \sqrt{64} = 8 \)
Square root of 121:	\( \sqrt{121} = 11 \)

2. Divide the square root of the numerator by the square root of the denominator:

\[ \sqrt{\frac{64}{121}} = \frac{\sqrt{64}}{\sqrt{121}} = \frac{8}{11} \]

Conclusion

The square root of \( \frac{64}{121} \) is \( \frac{8}{11} \).

The square root of \( \frac{64}{121} \) is a fundamental mathematical calculation that involves understanding both square roots and fractions. To find the square root of \( \frac{64}{121} \), one needs to compute the square roots of the numerator (64) and the denominator (121) separately. This process allows us to simplify the fraction and determine its square root as a fraction or a decimal.

Square roots represent a crucial concept in mathematics, particularly when dealing with fractions like \( \frac{64}{121} \). The square root of a number is a value that, when multiplied by itself, gives the original number. For \( \frac{64}{121} \), understanding how to calculate square roots helps in simplifying the fraction and determining its exact numerical value. This process involves basic arithmetic operations and knowledge of mathematical principles.

To find the square root of \( \frac{64}{121} \), follow these steps:

1. Calculate the square root of the numerator and the denominator separately:

Square root of 64:	\( \sqrt{64} = 8 \)
Square root of 121:	\( \sqrt{121} = 11 \)

2. Divide the square root of the numerator by the square root of the denominator:

\[ \sqrt{\frac{64}{121}} = \frac{\sqrt{64}}{\sqrt{121}} = \frac{8}{11} \]

The square root of \( \frac{64}{121} \) involves understanding the basic principles of square roots and fractions:

1. Identify the numerator and denominator: \( 64 \) and \( 121 \).
2. Calculate the square root of each:

   Square root of 64:	\( \sqrt{64} = 8 \)
   Square root of 121:	\( \sqrt{121} = 11 \)

3. Divide the square root of the numerator by the square root of the denominator:

\[ \sqrt{\frac{64}{121}} = \frac{\sqrt{64}}{\sqrt{121}} = \frac{8}{11} \]

This method demonstrates how to compute the square root of a fraction by breaking down the calculation into simpler steps.

The square root of \( \frac{64}{121} \) has several practical applications:

• Engineering: Engineers use square roots in calculations involving structural stability and material strength.
• Finance: Financial analysts use square roots in risk assessment and portfolio management.
• Physics: Physicists apply square roots in equations related to motion, energy, and waveforms.
• Medicine: Medical professionals use square roots in medical imaging and diagnostic procedures.

Understanding how to compute square roots of fractions enhances problem-solving abilities across various disciplines, making it a versatile mathematical skill.