Question

The value of $\sqrt{2\frac{1}{4}}\times {\left(1\frac{1}{3}\right)}^2+1÷3\sqrt{3\frac{3}{8}}=$

• A. $\frac{22}{9}$
• B. $\frac{10}{3}$
• C. $4\frac{1}{3}$
• D. $2\frac{1}{3}$

Answer 1

Answer: (A)

$\frac{22}{9}$

$\begin{array}{cc}& \sqrt{2\frac{1}{4}}\times {\left(1\frac{1}{3}\right)}^2+1÷3\sqrt{3\frac{3}{8}}\\ \Rightarrow & \sqrt{\frac{9}{4}}\times {\left(\frac{4}{3}\right)}^2+1÷3\sqrt{\frac{27}{8}}\\ \Rightarrow & \frac{3}{2}\times \frac{16}{9}+1÷\frac{3}{2}\\ \Rightarrow & \frac{8}{3}+1\times \frac{2}{3}=\frac{8+3}{3}\times \frac{2}{3}\\ \Rightarrow & \frac{22}{9}\end{array}$