Question

$$\sqrt{ 5 \frac{ 4 }{ 9 } }$$

Answer

(2*sqrt(5))/3

Solution


Use this rule: \(a \times \frac{b}{c}=\frac{ab}{c}\).
\[\sqrt{\frac{5\times 4}{9}}\]
Simplify  \(5\times 4\)  to  \(20\).
\[\sqrt{\frac{20}{9}}\]
Simplify.
\[\frac{\sqrt{20}}{\sqrt{9}}\]
Simplify  \(\sqrt{20}\)  to  \(2\sqrt{5}\).
\[\frac{2\sqrt{5}}{\sqrt{9}}\]
Since \(3\times 3=9\), the square root of \(9\) is \(3\).
\[\frac{2\sqrt{5}}{3}\]

Decimal Form: 1.490712