5.1 - Simplifying Radicals

5.1 - Simplifying Radicals

Steps for Simplifying Radical Expressions

• Use a factor tree to find the prime factorization of the number under the radical.

• Circle any pairs of numbers. Put one factor of each pair on the outside of the radical

• All uncircled numbers stay under the radical

• Simplify numbers outside of the radical and inside.

Simplify  using prime factorization

 $\sqrt{20}$                                            $\sqrt{108}$  



 $-5\sqrt{60}$                                    $\sqrt{54a^2b^2}$  



 $\sqrt{49x^3y^4}$                                   $\sqrt{2z}\cdot\sqrt{14z^3}$  

Simplify using Prime Factorization

 $-4\sqrt{8}\left(-5\sqrt{6}\right)$                                 $-3\sqrt{10ab}\cdot7\sqrt{30ab^2}$