Question

Simplify the following 3√28-5√63+4√112

Answer 1

7√7

using the ' rule of radicals '

• √a × √b ⇔ √ab

simplifying the radicals

√28 = √(4 × 7 ) = √4 × √7 = 2√7

√63 = √(9 × 7) =√9 × √7 = 3√7

√112 = √(16 × 7 ) = √16 × √7 = 4√7

substituting into the expression

3(2√7) - 5(3√7) + 4(4√7) = 6√7 - 15√7 + 16√7 = 7√7

Answer 2

First, simply each term. Then, add the coefficients of the like terms (same radicals).

`3√(28) = 3√(2*2*7) = 3(2)√(7) = 6√(7)`

`5√(63) = 5√(3*3*7) = 5(3)√(7) = 15√(7)`

`4√(112) = 4√(2*2*2*2*7) = 4(2*2)√(7) = 16√(7)`

*********************************************************

`3√(28) - 5√(63) + 4√(112)`

=
`6√(7) - 15√(7) + 16√(7)`

=
`(6 - 15 + 16)√(7)`

=
`7√(7)`