Review of Radicals

Perfect Square/Non Perfect Square Method

1) Find the largest perfect square the radicand is divisible by. Break the down the radical using this number.
2)Take the square root of the perfect square. Take it out of the radical.
3) Leave the "leftover" under the radical symbol.

​Use Method 1 to Simplify the radical

√32

​Use Method 1 to Simplify the radical

√180

​Factor Tree

1) Use a factor tree to simplify the radicand
2) Re-write the radicand as the product of all its factors from your tree. Look for pairs of square roots and use the rule above to simplify as far as you can.

​Use Method 2 to Simply the radical

√40

​Use Method 2 to Simply the radical

2√54

Steps to follow

1) Multiply numbers that are BOTH OUTSIDE the radical
2) Multiply numbers that are BOTH INSIDE the radical.
3) Simplify the expression.

​Simply

√6*4√6

​Simply

3√2*2√6

Steps to follow

1) Multiply numerator and denominator by a radical that will get rid of the radical in the denominator.
2) Simplify all the radicals
3) Simplify the fraction if needed.

​Simply

​Simply

​Simply