(English Medium) ICSE Class 9 - CISCE Question Bank Solutions

Write the lowest rationalising factor of : √18 - √50

Write the lowest rationalising factor of : √5 - √2

Write the lowest rationalising factor of : √13 + 3

Write the lowest rationalising factor of 15 – 3√2.

Write the lowest rationalising factor of : 3√2 + 2√3

Find the values of 'a' and 'b' in each of the following : 
`[2 + sqrt3]/[ 2 - sqrt3 ] = a + bsqrt3`

Find the values of 'a' and 'b' in each of the following:
`( sqrt7 - 2 )/( sqrt7 + 2 ) = asqrt7 + b` 

Find the values of 'a' and 'b' in each of the following: 
`3/[ sqrt3 - sqrt2 ] = asqrt3 - bsqrt2`

Find the values of 'a' and 'b' in each of the following:
`[5 + 3sqrt2]/[ 5 - 3sqrt2] = a + bsqrt2`

If x =`[sqrt5 - 2 ]/[ sqrt5 + 2]` and y = `[ sqrt5 + 2]/[ sqrt5 - 2 ]`; find :
x²

If x =`[sqrt5 - 2 ]/[ sqrt5 + 2]` and y = `[ sqrt5 + 2]/[ sqrt5 - 2 ]`; find : y²

If x =`[sqrt5 - 2 ]/[ sqrt5 + 2]` and y = `[ sqrt5 + 2]/[ sqrt5 - 2 ]`; find :  xy

If x =`[sqrt5 - 2 ]/[ sqrt5 + 2]` and y = `[ sqrt5 + 2]/[ sqrt5 - 2]`; find:

x² + y² + xy.

If m = `1/[ 3 - 2sqrt2 ] and n = 1/[ 3 + 2sqrt2 ],` find m²

If m = `1/[ 3 - 2sqrt2 ] and n = 1/[ 3 + 2sqrt2 ],` find n²

If m = `1/[ 3 - 2sqrt2 ] and n = 1/[ 3 + 2sqrt2 ],` find mn

If x = `2sqrt3 + 2sqrt2`, find: `1/x`

If x = 2√3 + 2√2, find: `(x + 1/x)`

If x = 2√3 + 2√2 , find : `( x + 1/x)^2`

If x = 1 - √2, find the value of `( x - 1/x )^3`