# rationalising the denominator

• Oct 1st 2005, 02:59 AM
x-disturbed-x
rationalising the denominator question? who knows
Given that (2+square root of 7)(4-square root of 7) = a + b(square root of 7)
a) find the value of a and value of b

b) given that 2+(square of 7) / 4+(square of 7) = c +d(square of 7) where c and d are rational numbers,

find the value of c and value of d.

ummmm..
• Oct 1st 2005, 04:14 AM
Cold
The first case involves multiplying out the brackets and then collecting like terms. You'll be able to collect terms with a factor of root 7.

The second case involves multipling the fraction by 1 expressed as ( 4 - root 7) / (4 - root 7). The point being that the denomitor can be multiplied out to remove the surd.
• Oct 1st 2005, 09:52 AM
ticbol
Given that (2+square root of 7)(4-square root of 7) = a + b(square root of 7)
a) find the value of a and value of b

[2 +sqrt(7)]*[4 -sqrt(7)] = a +b[sqrt(7)]
2*4 +2(-sqrt(7)) +sqrt(7)*4 +sqrt(7)*(-sqrt(7)) =
8 -2sqrt(7) +4sqrt(7) -7 =
1 +2sqrt(7) =

-----------------
b) given that 2+(square of 7) / 4+(square of 7) = c +d(square of 7) where c and d are rational numbers, find the value of c and value of d.

[2 +sqrt(7)] / [4 +sqrt(7)]
Rationalize the denominator. Multiply both numerator and denominator by the conjugant of the denominator, which is [4 -sqrt(7)],
= [2 +sqrt(7)]*[4 -sqrt(7)] / [4 +sqrt(7)]*[4 -sqrt(7)]
= [8 +2sqrt(7) -7] / [16 -7]
= [1 +2sqrt(7)] / 9
= (1/9) +(2/9)sqrt(7)
So, c = 1/9, and d = 2/9 ----------answer.