Question

What does it mean to rationalize the denominator when simplifying expressions with square roots?

Answer 1

When something says to 'rationalize the denominator,' when simplifying expressions with square roots, it is asking to get rid of any square roots in the denominator. This would put all of the square roots in the numerator, therefore only rational numbers would be in the denominator. We can rationalize the denominator by multiplying by the conjugate of the number in the denominator over itself (because that makes it a fraction equal to 1, and by multiplying by a fraction of 1, we don't change the value of the fraction).