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) Deleted for CBSE Board 2024 Exams
If x = 1/(2 − √3), find the value of x^3 − 2x^2 − 7x + 5 You are here
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
If x = 1/(2 − √3), find the value of x3 − 2x2 − 7x + 5 Let us first rationalise x x = 1/(2 − √3) = 1/(2 − √3) × (2 + √3)/(2 + √3) = (2 + √3)/(2^2 − (√3)^2 ) = (2 + √3)/(4 − 3) Now, x2 = (2 + √3)^2 = 〖2^2+(√3)〗^2 + 4√3 And, x3 = (2 + √3)^3 = 〖2^3+(√3)〗^3 + 3 × 2 × √3 (2 + √3) = 8+3√3 +6√3 (2 + √3) = 8+3√3 +12√3+18 Now, x3 − 2x2 − 7x + 5 = (26+15√3) − 2(7 +4√3) − 7(2 + √3 ) + 5 = 26+15√3 −14 −8√3−14−7√3+5 = (26+5−14−14)+(15√3 −8√3−7√3) = 𝟑