Question

Simplify the following:

`3sqrt(63) - 2sqrt(28) - sqrt(112)`

Answer 1

Given expression: `3sqrt(63) - 2sqrt(28) - sqrt(112)`

Step wise calculation:

1. Simplify each square root by factoring out perfect squares.

`sqrt(63)`

= `sqrt(9 xx 7)`

= `3sqrt(7)` 

`sqrt(28)`

= `sqrt(4 xx 7)`

= `2sqrt(7)`

`sqrt(112)`

= `sqrt(16 xx 7)`

= `4sqrt(7)`

2. Substitute back:

`3sqrt(63)`

= `3 xx 3sqrt(7)`

= `9sqrt(7)`

`-2sqrt(28)`

= `-2 xx 2sqrt(7)`

= `-4sqrt(7)`

`-sqrt(112)`

= `-4sqrt(7)`

3. Combine like terms all have `sqrt(7)`:

`9sqrt(7) - 4sqrt(7) - 4sqrt(7)`

= `(9 - 4 - 4)sqrt(7)`

= `1sqrt(7)`

= `sqrt(7)`