Question

Simplify:

`(sqrt(112) - sqrt(80))/(sqrt(63) - sqrt(45))`

Answer 1

`(sqrt(112) - sqrt(80))/(sqrt(63) - sqrt(45))`

Step 1: Simplify each square root

• `sqrt(112) = sqrt(16 xx 7) = 4sqrt(7)`
• `sqrt(80) = sqrt(16 xx 5) = 4sqrt(5)`
• `sqrt(63) = sqrt(9 xx 7) = 3sqrt(7)`
• `sqrt(45) = sqrt(9 xx 5) = 3sqrt(5)`

Step 2: Substitute back

`(sqrt(112) - sqrt(80))/(sqrt(63) - sqrt(45)) = (4sqrt(7) - 4sqrt(5))/(3sqrt(7) - 3sqrt(5))`

Step 3: Factor out common terms

Numerator: `4(sqrt(7) - sqrt(5))`

Denominator: `3(sqrt(7) - sqrt(5))`

`(4(sqrt(7) - sqrt(5)))/(3(sqrt(7) - sqrt(5)))`

Step 4: Cancel common factor

`4/3`