ADVANCED EXERCISES-Square Roots and Other Radicals

(2) Rationalize each expression.

SOLUTION: In each case, we need to multiply numerator and denominator by the conjugate of the expression with the square root(s).

1. The conjugate is . So rationalizing gives:
   
   

2. The conjugate is . So rationalizing gives:
   
   
   Note that in the fifth line, the numerator and the ( x² - 4 ) factor of the denominator are factored.