Date: Mon, 25 Jan 1999 16:10:26 -0600 (CST)
Subject: Simplifying Radicals

Name: Mary

Who is asking: Student
Level: Secondary

I would like to know how to simplify this question:

squareroot7 + squareroot3
I know the answer is (sqrt7 - sqrt3) but i would really love to know how to get that answer!! Thanks.


Hi Mary

Some people would argue that the expression is already simplified but in order to get the required answer you need to perform a process called "rationalizing the denominator". This is similar to the process that is used to "simplify" a fraction when the denominator is a decimal. For example

Here both the numerator and denominator have been multiplied by 100 to turn the denominator into a natural number. Likewise to simplify 4/sqrt7 you multiply the numerator and denominator by sqrt7 to get

   The simplest way to turn a binomial denominator with radical(s) into a rational number is to multiply the binomial by the same binomial expression with the opposite sign (+ instead of - or vice versa), called its conjugate. Here you will mult the numerator and denominator by (sqrt7 - sqrt3). So

Jack and Penny
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