Question

Evaluate 5√2 + √18

Please do not guess your answer, as I must get this problem correct, thank you!

Answer 1

`\large\boxed{5\sqrt2+√(18)=8\sqrt2}`

Explanation:

`5\sqrt2+√(18)=5\sqrt2+√(9\cdot2)\\\\\text{use}\ √(ab)=√(a)\cdot√(b)\\\\=5\sqrt2+\sqrt9\cdot\sqrt2=5\sqrt2+3\sqrt2=(5+3)\sqrt2=8\sqrt2`

Answer 2

8
`√(2)`

Explanation:

Using the rule of radicals

•
`√(a)` ×
`√(b)` ⇔
`√(ab)`, then

`√(18)`

=
`√(9(2))` =
`√(9)` ×
`√(2)` = 3
`√(2)`

Hence

5
`√(2)` + 3
`√(2)` = 8
`√(2)` ≈ 11.31