Question

I missed the class on rationalising denominators.

Can anyone please help me with these three maths along with explanations.

Answer 1

see attached

Explanation:

Answer 2

`4√(3)`

`(5 - √(3))/(11)`

`(11(3 + √(5)))/(8)`

Explanation:

If you have a simple square root in the denominator, multiply the fraction by a fraction that is the root over the root.

`(12)/(√(3)) =`

`= (12)/(√(3)) * (√(3))/(√(3))`

`= (12√(3))/(√(3)√(3))`

`= (12√(3))/(3)`

`= 4√(3)`

If you have a denominator consisting of a rational number plus a root, multiply the fraction by a fraction that is the denominator over the denominator in which you change only the sign outside the root.

`(2)/(5 + √(3)) =`

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

`= (2(5 - √(3)))/((5 + √(3))(5 - √(3)))`

`= (2(5 - √(3)))/(25 - 3)`

`= (2(5 - √(3)))/(22)`

`= (5 - √(3))/(11)`

`(11)/(6 - 2√(5)) =`

`= (11)/(6 - 2√(5)) * (6 + 2√(5))/(6 + 2√(5))`

`= (11(6 + 2√(5)))/((6 - 2√(5))(6 + 2√(5)))`

`= (22(3 + √(5)))/(36 - 4 * 5)`

`= (22(3 + √(5)))/(36 - 20)`

`= (22(3 + √(5)))/(16)`

`= (11(3 + √(5)))/(8)`