Question

rationalise the denominator of 6-4√2/6+4√2

Answer 1

(6-4√2)/(6+4√2)

Rationalising factor = 6-4√2

(6-4√2)/(6+4√2) × (6-4√2)/(6-4√2)

=(6-4√2)(6-4√2)/(6+4√2)(6-4√2)

=(6-4√2)²/(6²-(4√2)²)

=[6²+(4√2)²-2(6)(4√2)]/(36-16(2))

=(36+16(2)-48√2)/(36-32)

=(36+32-48√2)/4

=(68-48√2)/4

=68/4 - 48√2/4

= 17 - 12√2

Hope it helps

Answer 2

(6-4√2)/(6+4√2
==============
(6-4√2)/(6+4√2) × (6-4√2)/(6-4√2)
=(6-4√2)(6-4√2)/(6+4√2)(6-4√2)
=(6-4√2)²/(6²-(4√2)²)
=[6²+(4√2)²-2(6)(4√2)]/(36-16(2))
=(36+16(2)-48√2)/(36-32)
=(36+32-48√2)/4
=(68-48√2)/4
=68/4 - 48√2/4
= 17 - 12√2