Write the simplest form of rationalising factor for the given surd. 4 sqrt 11 - Algebra

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

`4 sqrt 11`

Sum

Since `4sqrt11 xx sqrt11 = 4 xx 11 = 44` is a rational number.

So, `sqrt 11` is the simplest form of rationalising factor.

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Rationalisation of Surds

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Chapter 2: Real Numbers - Problem Set 2 [Page 35]

Chapter 2 Real Numbers
Problem Set 2 | Q (6) (vi) | Page 35

Rationalize the denominator.

`5/sqrt 7`

Write the lowest rationalising factor of 5√2.

Write the lowest rationalising factor of : 15 - 3√2

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

If `[ 2 + sqrt5 ]/[ 2 - sqrt5] = x and [2 - sqrt5 ]/[ 2 + sqrt5] = y`; find the value of x² - y².

Evaluate : `( 4 - √5 )/( 4 + √5 ) + ( 4 + √5 )/( 4 - √5 )`

Rationalise the denominator `5/(3sqrt(5))`

If x = `sqrt(5) + 2`, then find the value of `x^2 + 1/x^2`