Multiplying & Dividing Radicals

Operations with Radicals (Square Roots) Essential Question How do I multiply and divide radicals?

The multiplication property is often written: or

* Multiplying Radicals To multiply radicals: multiply the coefficients (the numbers on the outside) and then multiply the radicands (the numbers on the inside) and then simplify the remaining radicals.

Multiply and then simplify

Trick Question Is there a number in front of √7 ? Hint: Is there a number in front of x? The answer is 1. Just as there is a “ghost 1” in front of the x, there is also a “ghost 1” in front of the √7

A related property says that square roots are also distributive over division:

or

Dividing Radicals To divide radicals: divide the coefficients (the numbers on the outside), divide the radicands (the numbers on the inside) if possible, and rationalize the denominator so that no radical remains in the denominator

That was easy!

42 cannot be simplified, so we are finished. This cannot be divided which leaves the radical in the denominator. We do not leave radicals in the denominator. So we need to rationalize by multiplying the fraction by something so we can eliminate the radical in the denominator. 42 cannot be simplified, so we are finished.

This can be divided which leaves the radical in the denominator This can be divided which leaves the radical in the denominator. We do not leave radicals in the denominator. So we need to rationalize by multiplying the fraction by something so we can eliminate the radical in the denominator.

This cannot be divided which leaves the radical in the denominator This cannot be divided which leaves the radical in the denominator. We do not leave radicals in the denominator. So we need to rationalize by multiplying the fraction by something so we can eliminate the radical in the denominator. Reduce the fraction.