Multiplying Radicals Worksheet

Multiplying Radicals

Simplify each expression. Show all your work. Remember to simplify radicals by factoring out perfect squares.

1. Multiply the following expressions:

a) \(\sqrt{3} \cdot \sqrt{12}\)

b) \(2\sqrt{5} \cdot 3\sqrt{10}\)

c) \(\sqrt{6}( \sqrt{3} + \sqrt{2})\)

d) \((4 + \sqrt{7})(4 - \sqrt{7})\)

2. Complete the following statements about multiplying radicals:

a) To multiply radicals, you multiply the coefficients (numbers   the radical) and then multiply the radicands (numbers   the radical).

b) After multiplying, always remember to   the radical expression by factoring out any     from the radicand.

c) The product of \(\sqrt{a} \cdot \sqrt{a}\) is equal to  .

3. Which of the following is the simplified product of \((2\sqrt{3})(5\sqrt{6})\)?

4. Find the area of a rectangle with a length of \((3 + \sqrt{5})\) units and a width of \((2 - \sqrt{5})\) units. Express your answer in simplest radical form.