Question

The square root of $\frac{{\left(3\frac{1}{4}\right)}^4-{\left(4\frac{1}{3}\right)}^4}{{\left(3\frac{1}{4}\right)}^2-{\left(4\frac{1}{3}\right)}^2}$ is

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

Answer 1

The correct option is C $5\frac{5}{12}$

Given expression can be simplified as ${\left(3\frac{1}{4}\right)}^2+{\left(4\frac{1}{3}\right)}^2$
$={13}^2(\frac{1}{16}+\frac{1}{9})=169\times \frac{25}{144}$
Square root is $=13\times \frac{5}{12}=5\frac{5}{12}$