Question

Work out the value of (square root 99 - square root 11)^2

Answer 1

44

Explanation:

using the rules of radicals

• (
`√(x)` )² = x

•
`√(a)` ×
`√(b)` =
`√(ab)`

given

(
`√(99)` -
`√(11)` )²

= (
`√(99)` -
`√(11)` )(
`√(99)` -
`√(11)` ) ← expand using FOIL

= (
`√(99)` )² - 2.
`√(99)` .
`√(11)` + (
`√(11)` )²

= 99 - 2 .
`√(99(11))` + 11

= 99 - 2 .
`√(1089)` + 11

= 99 - 2(33) + 11

= 99 - 66 + 11

= 33 + 11

= 44