We do not leave an irrational number in the denominator.
So, we rationalise the denominator. Let us look at some examples
Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class
Rationalising
Add (3√2+7√3) and (√2−5√3)
Divide 5√11 by 3√33
Multiply 2√15 by 7√5
Simplify (√5+√7)^2
Simplify (√4−√13)(√4+√13)
Simplify (9−√3)(9+√3)
Simplify (3√5−5√2)(4√5+3√2)
Rationalise the denominator of 8/√7
Rationalise the denominator of 1/((8 + 5√2))
Simplify (7√3)/(√10 + √3)−(2√5)/(√6 + √5)−(3√2)/(√15 + 3√2)
Multiple Choice Questions - Chapter 1 Class 9 Maths
Example 16
If a and b are rational numbers and (√11 − √7)/(√11 + √7) = a – b√77, find the value of a and b
Example 17
Find the values of a and b if (7 + 3√5)/(3 + √5) – (7 − 3√5)/(3 − √5) = a+√5 b
Ex 1.4, 5 (i)
If x = 1/(2 − √3), find the value of x^3 − 2x^2 − 7x + 5
If a = 5 + 2√6 and b = 1/a, then what will be the value of a^2+b^2 ?
Example 18
Example 19 Important
Rationalising
Last updated at May 29, 2023 by Teachoo
We do not leave an irrational number in the denominator.
So, we rationalise the denominator. Let us look at some examples
Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class
Some Identities (√𝑎)^2=𝑎 √(𝑎^2 )=𝑎 √𝑎𝑏=√𝑎 ×√𝑏 √(𝑎/𝑏)=√𝑎/√𝑏 (√𝑎−√𝑏)(√𝑎+√𝑏)=𝑎−𝑏 (𝑎−√𝑏)(𝑎+√𝑏)=𝑎^2−𝑏 (√𝑎+√𝑏)^2=𝑎+𝑏+2√𝑎𝑏 (√𝑎+√𝑏)(√𝑐+√𝑑)=√𝑎𝑐+√𝑎𝑑 + √𝑏𝑐 + √𝑏𝑑