Last updated at Sept. 11, 2020 by Teachoo

Transcript

If a = 5 + 2β6 and b = 1/π, then what will be the value of π^2+π^2 ? a = 5 + 2β6 b = 1/π = 1/(5 + 2β6) = 1/(5 + 2β6) Γ (5 β 2β6)/(5 β 2β6) = (5 β 2β6)/(5^2 β (2β6)^2 ) = (5 β 2β6)/(25 β 24) We know that γ(π+π)γ^2 = π^2+π^2+ 2ππ π^π+π^π = γ(π+π)γ^π β πππ Here, π+π = (5+2β6)+5(5β2β6) ππ = (5+2β6) (5β2β6) Thus, π^2+π^2 = γ(π+π)γ^2 β 2ππ π^2+π^2=γ10γ^2β2 Γ 1 =100β2 =ππ

Rationalising

Rationalising denominator of irrational number

Add (3β2+7β3) and (β2β5β3)

Divide 5β11 by 3β33

Multiply 2β15 by 7β5

Simplify (β5+β7)^2

Simplify (β4ββ13)(β4+β13)

Simplify (9ββ3)(9+β3)

Simplify (3β5β5β2)(4β5+3β2)

Rationalise the denominator of 8/β7

Rationalise the denominator of 1/((8 + 5β2))

Multiple Choice Questions - Chapter 1 Class 9 Maths

Simplify (7β3)/(β10 + β3)β(2β5)/(β6 + β5)β(3β2)/(β15 + 3β2)

If a and b are rational numbers and (β11 β β7)/(β11 + β7) = a β bβ77, find the value of a and b

Example 17

Example 18

Find the values of a and b if (7 + 3β5)/(3 + β5) β (7 β 3β5)/(3 β β5) = a+β5 b

Ex 1.5,5 Important

If x = 1/(2 β β3), find the value of x^3 β 2x^2 β 7x + 5

Example 19 Important

If a = 5 + 2β6 and b = 1/a, then what will be the value of a^2+b^2 ? You are here

Example 20

Chapter 1 Class 9 Number Systems

Concept wise

- Rational numbers - Definition
- Finding rational number between two numbers
- Irrational Numbers
- Simplifying real numbers
- Rationalising
- Laws of exponents
- Finding decimal expansion
- Expressing decimal in p/q
- Classifiying rational/irrational
- Finding irrational numbers b/w two numbers
- Real numbers on a number line

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.