Question

simplify $\sqrt{80} + \sqrt{2\frac{2}{9}$

Answer 1

Answer:

$\displaystyle \frac{14}{3}\sqrt{5}$

Step-by-step explanation:

Simplify:

$\displaystyle \sqrt{80} + \sqrt{2\frac{2}{9}}$

We must express the mixed fraction into an improper fraction:

$2\frac{2}{9}=2+\frac{2}{9}=\frac{20}{9}$

$\displaystyle \sqrt{80} + \sqrt{2\frac{2}{9}}=\displaystyle \sqrt{80} + \sqrt{\frac{20}{9}}$

Since 80 = 16*5 and 20=4*5

$\displaystyle \sqrt{80} + \sqrt{2\frac{2}{9}}=\displaystyle \sqrt{16*5} + \sqrt{\frac{4*5}{9}}$

$\displaystyle \sqrt{80} + \sqrt{2\frac{2}{9}}=\displaystyle 4\sqrt{5} + \frac{2}{3}\sqrt{5}$

Adding the fractions:

$\displaystyle \sqrt{80} + \sqrt{2\frac{2}{9}}=\displaystyle (4 + \frac{2}{3})\sqrt{5}$

$\mathbf{\displaystyle \sqrt{80} + \sqrt{2\frac{2}{9}}=\displaystyle \frac{14}{3}\sqrt{5}}$