Question

Simplify
`√(80) + \sqrt{2(2)/(9)`

Answer 1

`\displaystyle (14)/(3)√(5)`

Explanation:

Simplify:

`\displaystyle √(80) + \sqrt{2(2)/(9)}`

We must express the mixed fraction into an improper fraction:

`2(2)/(9)=2+(2)/(9)=(20)/(9)`

`\displaystyle √(80) + \sqrt{2(2)/(9)}=\displaystyle √(80) + \sqrt{(20)/(9)}`

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

`\displaystyle √(80) + \sqrt{2(2)/(9)}=\displaystyle √(16*5) + \sqrt{(4*5)/(9)}`

`\displaystyle √(80) + \sqrt{2(2)/(9)}=\displaystyle 4√(5) + (2)/(3)√(5)`

Adding the fractions:

`\displaystyle √(80) + \sqrt{2(2)/(9)}=\displaystyle (4 + (2)/(3))√(5)`

`\mathbf{\displaystyle √(80) + \sqrt{2(2)/(9)}=\displaystyle (14)/(3)√(5)}`