Question

Simply and show how you got the answer

Answer 1

Problem 1.

`(3)/( √(5) - 2 )`

Rationalize the denominator by multiplying the numerator and denominator by the denominator. (Important: if the denominator has a minus sign, change to plus and vice versa)

`⟹(3 * √(5 + 2) )/( (√(5) - 2 ) * ( √(5) + 2) )`

`⟹ (3 √(5) + 6 )/( √(25) + 2 √(5) - 2 √(5) - 4 ) ⟹(3 √(5) + 6 )/(5 - 4)`

`⟹(3 √(5) + 6)/(1) ⟹3 √(5) + 6`

Problem 2.

`(6 - √(12) )/( √(3) + √(10) )`

Rationalize the denominator.

`⟹((6 - √(12) ) * ( √(3) - √(10) ))/( (√(3) + √(10) ) * ( √(3) - √(10) )`

`⟹(6 √(3) - 6 √(10) - √(36) + √(120) )/( √(9) - √(30) + √(30) - √(100) )`

`⟹ (6 √(3) - 6 √(10) - √(36) + √(120) )/(3 - 10) ⟹ (6 √(3) - 6 √(10) - √(36) + √(120) )/( - 7)`

`⟹(6 √(3) - 6 √(10) - 6 + √(12 * 10) )/( - 7)⟹(6 √(3) - 6 √(10) - 6 + 4 √(3 * 10) )/( - 7)`

`⟹ - (6 √(3) - 6 √(10) - 6 + 2 √(30) )/(7)`

Therefore:

1.
`3 √(5) + 6`

2.
`- (6 √(3) - 6 √(10) - 6 + 2 √(30) )/(7)`

I hope these help