Write the Lowest Rationalising Factor of : 7 - √7 - Mathematics

Write the lowest rationalising factor of : 7 - √7

Sum

7 - √7
( 7 - √7 )( 7 + √7 ) = 49 - 7 = 42
Therefore, lowest rationalizing factor is ( 7 + √7 ).

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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 2.4 | Page 21

Rationalize the denominator.

`6/(9sqrt 3)`

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

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

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

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

Show that :
`1/[ 3 - 2√2] - 1/[ 2√2 - √7 ] + 1/[ √7 - √6 ] - 1/[ √6 - √5 ] + 1/[√5 - 2] = 5`

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

If √2 = 1.4 and √3 = 1.7, find the value of : `1/(3 + 2√2)`

Rationalise the denominator `(3sqrt(5))/sqrt(6)`

Given `sqrt(2)` = 1.414, find the value of `(8 - 5sqrt(2))/(3 - 2sqrt(2))` (to 3 places of decimals).