Question

Rationalise the following​

Answer 1

Step-by-step explanation:

Solution :-

Method-1:-

See the above attachment

Method-2:-

Given that

[1/(√4+√5)]+[1/(√5+√6)]+[1/(√6+√7)]+[1/(√7+√8)]

+[1/(√8+√9]

We know that

The Rationalising factor of√a+√b =√a-√b

Rationalising factor of √4+√5 =√4-√5

Rationalising factor of √5+√6=√5-√6

Rationalising factor of √6+√7 = √6-√7

Rationalising factor of√7+√8 =√7-√8

Rationalising factor of√8+√9 =√8-√9

On Rationalising the each denominator then

I. 1/(√4+√5)]×[(√4-√5)/(√4-√5)]

=> (√4-√5)/(4-5)

=> (√4-√5)/-1

=√5-√4-------(1)

II. [1/(√5+√6)]×[(√5-√6)/(√5-√6)]

=>(√5-√6)/(5-6)

=>(√5-√6)/-1

=>√6-√5-------(2)

III. [1/(√6+√7)]×[(√6-√7)/(√6-√7)]

=>(√6+√7)/(6-7)

=>(√6-√7)/-1

=>√7-√6------(3)

IV. [1/(√7+√8)]×[(√7-√8)/(√7-√8)]

=>(√7-√8)/(7-8)

=>(√7-√8)/-1

=>√8-√7--------(4)

V. [1/(√8+√9]×[(√8-√9)/(√8-√9)]

=>(√8-√9)/(8-9)

=>(√8-√9)/-1

=>√9-√8------(5)

On adding above all

=>√5-√4+√6-√5+√7-√6+√8-√7+√9-√8

=>√9-√4

=>3-2

=1

Answer:-

The answer for the given problem is 1

Used formulae:-

1.The Rationalising factor of√a+√b =√a-√b

2.(a+b)(a-b)=a^2-b^2