Question

Simplify the following:

`sqrt(175) - sqrt(112) - sqrt(28) + sqrt(63)`

Answer 1

`sqrt(175) - sqrt(112) - sqrt(28) + sqrt(63)`

Step 1: Break each term into factors of perfect squares

`sqrt(175) = sqrt(25 xx 7) = 5sqrt(7)`

`sqrt(112) = sqrt(16 xx 7) = 4sqrt(7)`

`sqrt(28) = sqrt(4 xx 7) = 2sqrt(7)`

`sqrt(63) = sqrt(9 xx 7) = 3sqrt(7)`

Step 2: Substitute back

`5sqrt(7) - 4sqrt(7) - 2sqrt(7) + 3sqrt(7)`

Step 3: Combine like terms

`(5 - 4 - 2 + 3)sqrt(7) = 2sqrt(7)`