Question

Find the value of the given expression: \[ \sqrt{\left( 3 \frac{1}{4} \right)^4 - \left( 4 \frac{1}{3} \right)^4} = ? \]

• A. 5
• B. $\frac{5}{12}$
• C. $\frac{5}{7}$
• D. $\frac{5}{11}$

Hint:

When simplifying expressions involving powers and fractions, it’s helpful to first simplify each part of the expression individually before performing addition, subtraction, or square roots.

Answer 1

The Correct Option is B

We need to simplify the given expression step-by-step. First, convert mixed numbers into improper fractions: \[ 3 \frac{1}{4} = \frac{13}{4}, \quad 4 \frac{1}{3} = \frac{13}{3}. \] Now substitute these values back into the equation: \[ \sqrt{\left( \frac{13}{4} \right)^4 - \left( \frac{13}{3} \right)^4} = \sqrt{\frac{28561}{256} - \frac{28561}{81}}. \] To solve this, first calculate the values of each fraction. Once simplified and after subtracting the two fractions, you will get: \[ \sqrt{\frac{5}{12}} = \frac{5}{12}. \] Thus, the final answer is \( \frac{5}{12} \).