Question

rationalise the denominator 6-4√2÷6+4√2

Answer 1

Hi friend,
(6 - 4 √ 2) / (6 + 4 √ 2) * (6 -4 √ 2) / ( 6 - 4 √ 2)

= ( 6 - 4√ 2)2 / [ 62 - (4√ 2)2 ]

= 36 + 32 - 48√ 2 / [ 36 - 32 ]

= 68 - 48√ 2 / 4

= 4(17 - 12√ 2) / 4

= 17 -  12√ 2

Hope this helps.

Answer 2

6-4√3 ÷ 6+4√2
For rationalising we take the denominator for multiplying but by just changing the side in between to make it a rational number
So 6-4√2÷6+4√2 ×6-4√2÷ 6-4√2
Now by identity (a-b)(a-b)=(a-b)*2 and a-b(a+b=a*2-b*2
We get
(6-4√2)*2/(6)*2-(4√2)*2
36+32-48√2. /36 -32
68-48√2 /4
Taking 4 common from numerator
We get
4(17-12√2) /4
17-12√2