How to Rationalize the Denominator

Rationalize means to make the denominator (of a fraction) a rational number.



In terms of algebraic expressions it is to try and remove the square root √, ₂√, ₃√ from an equation, with out changing the value of the expression.

And again, basically, its trying to make an expression that has a square root on the bottom of a fraction disappear. Thats without changing the value of the expression.






Example 1 : Rationalize 4√2



First, multiply the top and bottom of the above expression by √2 to give : 4×√2√2×√2



Then using One of the rules of surds that √a×√b=√ab

The bottom part of the fraction equals 2, using the above rule since √2×√2=√4=2

= 4√22



Next cancel the top and bottom numbers to give 2√2

Therefore 4√2=2√2





To rationalize an algebraic expression




Example 2 : √(x-2)=x Rationalizes into x-2=x²

or x²-x+2=0




Example 3 : ∛(x²+1)=2 Rationalizes into x²+1=8 or x²-7=0










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