Question

Expand and simplify (√3+√5)^2​

Answer 1

8 + 2
`√(15)`

Explanation:

Using the rules of radicals

`√(a)` ×
`√(b)` ⇔
`√(ab)`

`√(a)` ×
`√(a)` = a

Given

(
`√(3)` +
`√(5)` )² = (
`√(3)` +
`√(5)` )(
`√(3)` +
`√(5)` )

Each term in the second factor is multiplied by each term in the first factor

`√(3)` (
`√(3)` +
`√(5)`) +
`√(5)`(
`√(3)` +
`√(5)`) ← distribute parenthesis

= 3 +
`√(15)` +
`√(15)` + 5 ← collect like terms

= 8 + 2
`√(15)`