Rationalising denominator of irrational number

Last updated at August 14, 2026 by

Rationalising denominator of irrational number - Rationalising

We do not leave an irrational number in the denominator.

So, we rationalise the denominator.  Let us look at some examples

  1. Rationalise 1/√2
  2. Rationalise 1/2 +√3
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Transcript

Some Identities (√𝑎)^2=𝑎 √(𝑎^2 )=𝑎 √𝑎𝑏=√𝑎 ×√𝑏 √(𝑎/𝑏)=√𝑎/√𝑏 (√𝑎−√𝑏)(√𝑎+√𝑏)=𝑎−𝑏 (𝑎−√𝑏)(𝑎+√𝑏)=𝑎^2−𝑏 (√𝑎+√𝑏)^2=𝑎+𝑏+2√𝑎𝑏 (√𝑎+√𝑏)(√𝑐+√𝑑)=√𝑎𝑐+√𝑎𝑑 + √𝑏𝑐 + √𝑏𝑑

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