Question

Simplify the expression,

Assume all variables are positive.

Answer 1

x²
`√(5)`

Explanation:

using the rule of radicals

`√(a)` ×
`√(b)` ⇔
`√(ab)`

given

5
`√(20x^4)` - 3
`√(45x^4)`

simplify the 20 and 45 inside the radicals

`√(20)` =
`√(4(5))` =
`√(4)` ×
`√(5)` = 2
`√(5)`

`√(45)` =
`√(9(5))` =
`√(9)` ×
`√(5)` = 3
`√(5)`

Then

= 5(2
`√(5)` x² ) - 3(3
`√(5)` x² )

= 10
`√(5)` x² - 9
`√(5)` x²

= x²
`√(5)`