Question

Rationalise the denominator of
2√3 + 3√2/4√3 +√2

Answer 1

`(9+ 5√(6) )/(23)`

Explanation:

2√3 + 3√2 * 4√3 -√2

4√3 +√2 4√3 -√2

multiply by conjugate

2√3 + 3√2 * 4√3 -√2 = 18 +10√6 = 9 +5√6

4√3 +√2 4√3 -√2 46 23

Answer 2

Explanation:

To rationalize the denominator, multiply the numerator and denominator by the conjugate of the denominator.

Conjugate of 4√3 + √2 is 4√3 - √2

(2√3 +3 √2)(4√3 - √2) = (2√3 * 4√3) - (2√3*√2) + (3√2*4√3) -(3√2*√2) {Use FOIL method}

= 8*3 - 2*√6+12√6 -3*2

= 24 -2√6 +12√6 - 6

= 24 - 6 + (-2+12)√6)

= 18 + 10√6

`(2√(3)+3√(2) )/((4√(3)+√(2) )\\\\=((2√(3)+3√(2))(4√(3)-√(2)) )/((4√(3)+√(2) )(4√(3)-√(2) ))\\\\=(18+10√(6) )/((4√(3))^(2)-(√(2))^(2) )\\\\=(18+10√(6) )/(48-2)\\\\=(18+10√(6) )/(46)\\\\\\=(2(9+5√(6) ))/(46)\\\\=(9+5√(6) )/(23)`