Review of Radicals

Review of Radicals

Simplifying Radicals Method 1

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.

Example

​Use Method 1 to Simplify the radical

√32

Example

​Use Method 1 to Simplify the radical

√180

Math Response

Simplify using Method 1

√72

Type answer here

Correct Answer: 6\sqrt{2}

Deg^°

Rad

Math Response

Simplify using Method 1

√147

Type answer here

Correct Answer: 7\sqrt{3}

Deg^°

Rad

Simplifying Radicals Method 2

​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.

Example

​Use Method 2 to Simply the radical

√40

Example

​Use Method 2 to Simply the radical

2√54

Math Response

Simplify using Method 2

√48

Type answer here

Correct Answer: 4\sqrt{3}

Deg^°

Rad

Math Response

Simplify using Method 2

8√128

Type answer here

Correct Answer: 64\sqrt{2}

Deg^°

Rad

Operations with Radicals

Multiplying Radicals

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.

Example

​Simply

√6*4√6

Example

​Simply

3√2*2√6

Math Response

Simplify

4√8*√10

Type answer here

Correct Answer: 16\sqrt{5}

Deg^°

Rad

Rationalizing the Denominator

Rationalizing the Denominator

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.

Example

​Simply

Example

​Simply

Example

​Simply

Math Response

Simplify

$$\frac{2}{\sqrt[]{3}}$$

Type answer here

Correct Answer: \frac{2\sqrt{3}}{3}

Deg^°

Rad

Math Response

Simplify

$$\frac{6}{\sqrt[]{2}}$$

Type answer here

Correct Answer: 3\sqrt{2}

Deg^°

Rad