Question

Simplify 1by√6+√5-√11

Answer 1

= 1(√6+√5-√11)

Here,we need to rationalise the denominator.

Rationalising factor = √6+√5+√11

= 1/(√6+√5-√11) × (√6+√5+√11)/(√6+√5+√11)

=1(√6+√5+√11)/(√6+√5-√11)(√6+√5+√11)

=(√6+√5-√11)/[(√6+√5)²-(√11)²]

=(√6+√5-√11)/[(√6²+√5²+2(√6)(√5)) - √11²]

=(√6+√5-√11)/[(6+5+2√30 - 11)]

=(√6+√5-√11)/(11+2√30-11)

=(√6+√5-√11)/2√30

The denominator is still irrational, so we need to rationalise it further.

Now,the rationalising factor = √30

=(√6+√5-√11)/2√30 × √30/√30

=(√6+√5-√11)(√30)/(2√30)(√30)

=(√6×30+√5×30-√11×30)/2√30²

=(√6×6×5+√5×5×6-√330)/2(30)

=(6√5+5√6-√330)/60

Now,the denominator is rationalised.

Hence,it is simplified.

✪hope it helps✪

✰Snehitha✰

✰Brainly benefactor✰