Saturday, March 16, 2013

Q13/028) Rationalise the denominator 1/(√2 +√3 +√5)?

This type is done one at a time
(√2 +√3 +√5) = (√2 +√3) +√5)

so multiply both numerator and denominator by (√2 +√3) -√5)

to get ((√2 +√3) -√5))/(( (√2 +√3)^2 -√5) ((√2 +√3) +√5))
= ((√2 +√3) -√5))/((√2 +√3)^2 -5)
= ((√2 +√3) -√5))/((2 +3+ 2√6 -5)
= ((√2 +√3) -√5))/(2√6)

now multiply both numerator and denominator by √6

to get √6((√2 +√3) -√5))/12

5 comments:

IrizuMC said...

Our teacher told us to multiply the numerator and denominator with √2+√3-√5 and i was getting 2√6 as the denominator. I didn't think of multiplying it with √6.
Can we substitute approximate values for √2, √3 and √5, sum them (we get 5.39 approximately) and write the answer as 1/5 (by rounding off 5.39)?

Unknown said...

Could u solve for the same values but root 5 instead of-√5

Unknown said...

Nice

Unknown said...

Can you do it with -√2+√3-√5

kaliprasad said...

it can be done.
As -√2+√3-√5 = √3-(√5 + √2) so you need to multiply numerator and denominator by √3+ (√5 + √2