Answer
True
Work Step by Step
To simplify the expression, we will first use the rule $\sqrt \frac{a}{b}=\frac{\sqrt a}{\sqrt b}$:
$\sqrt {\frac{1}{4}}+\sqrt[3] \frac{1}{8}+\sqrt \frac{4}{9}$
=$\frac{\sqrt 1}{\sqrt 4}+\frac{\sqrt[3] 1}{\sqrt[3] 8}+\frac{\sqrt 4}{\sqrt 9}$
=$\frac{\sqrt 1}{\sqrt 4}+\frac{\sqrt[3] 1}{\sqrt[3] {2^{3}}}+\frac{\sqrt 4}{\sqrt 9}$
Next, we simplify the expression:
=$\frac{\sqrt 1}{\sqrt 4}+\frac{\sqrt[3] 1}{\sqrt[3] {2^{3}}}+\frac{\sqrt 4}{\sqrt 9}$
=$\frac{1}{2}+\frac{1}{2}+\frac{2}{3}$
Then, we take LCM of the denominators of the fractions to add the fractions. Upon observation, the LCM is found to be 6:
=$\frac{1}{2}+\frac{1}{2}+\frac{2}{3}$
=$\frac{3(1)+3(1)+2(2)}{6}$
=$\frac{3+3+4}{6}$
=$\frac{10}{6}$
=$\frac{5}{3}$
