Write the Lowest Rationalising Factor of : √13 + 3

Write the lowest rationalising factor of : √13 + 3

Sum

( √13 + 3 )( √13 - 3 ) = ( √13 )² - 3² = 13 - 9 = 4

Its lowest rationalizing factor is √13 - 3.

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Rationalisation of Surds

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Chapter 1: Rational and Irrational Numbers - Exercise 1 (C) [Page 21]

Chapter 1 Rational and Irrational Numbers
Exercise 1 (C) | Q 2.7 | Page 21

Rationalize the denominator.

`3 /sqrt5`

Write the simplest form of rationalising factor for the given surd.

`3/5 sqrt 10`

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

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

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

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

If x = 5 - 2√6, find `x^2 + 1/x^2`

Rationalise the denominator `sqrt(75)/sqrt(18)`

Rationalise the denominator and simplify `sqrt(5)/(sqrt(6) + 2) - sqrt(5)/(sqrt(6) - 2)`

Find the value of a and b if `(sqrt(7) - 2)/(sqrt(7) + 2) = asqrt(7) + b`.