1.5a: Simplifying Radicals...1.6a_simplifying radicals.notebook October 23, 2014 Simplifying...

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1.6a_simplifying radicals.notebook October 23, 2014 1.5a: Simplifying Radicals

Transcript of 1.5a: Simplifying Radicals...1.6a_simplifying radicals.notebook October 23, 2014 Simplifying...

1.6a_simplifying radicals.notebook October 23, 2014

1.5a: Simplifying Radicals

1.6a_simplifying radicals.notebook October 23, 2014

List All of the Perfect Squares to 400

1.6a_simplifying radicals.notebook October 23, 2014

Radical Symbol:

The square root symbol

Radicand:

The number in the radical

5

1.6a_simplifying radicals.notebook October 23, 2014

Number of Solutions

• Even roots have two solutions; one positive and one negative

EX.

**The radicand of an even root can't be negative. Why???

1.6a_simplifying radicals.notebook October 23, 2014

Principle Root­the nonnegative root of a number

What does this mean?

Principle square root

Opposite of principle square root

both square roots

1.6a_simplifying radicals.notebook October 23, 2014

Taking Roots of Variables• Just divide the exponent by the index!

• Example: x8 = x2

1.6a_simplifying radicals.notebook October 23, 2014

Examples:

1. 81n2

2. - (x+1) 4

3. 3

8n9

4. 4

m8n4

1.6a_simplifying radicals.notebook October 23, 2014

Try These:

1. ­ √121a6c2

2. √169 +_

3. √(8x -2)2

4. √(2x - 7)66

1.6a_simplifying radicals.notebook October 23, 2014

Simplifying Radicals1. First see if the number is a perfect square

2. If it's not a perfect square, divide the radicand by the biggest perfect square that will go into it evenly

3. Next, simplify the perfect square

***For a radical to be in simplest form, the radicand cannot be divisible by any perfect squares

1.6a_simplifying radicals.notebook October 23, 2014

A radical is simplified when:

1. There are no perfect square factors.

2. There are no fractions under the radical sign.

3. There are no radicals in the denominator.

1.6a_simplifying radicals.notebook October 23, 2014

Ex 5: Simplify.Simplifying Radicals1. First see if the number is a perfect square

2. If it's not a perfect square, divide the radicand by the biggest perfect square that will go into it evenly

3. Next, simplify the perfect square

***For a radical to be in simplest form, the radicand cannot be divisible by any perfect squares

1.6a_simplifying radicals.notebook October 23, 2014

Ex 6: Simplify. Simplifying Radicals1. First see if the number is a perfect square

2. If it's not a perfect square, divide the radicand by the biggest perfect square that will go into it evenly

3. Next, simplify the perfect square

***For a radical to be in simplest form, the radicand cannot be divisible by any perfect squares

1.6a_simplifying radicals.notebook October 23, 2014

Ex 7: Simplify. Simplifying Radicals1. First see if the number is a perfect square

2. If it's not a perfect square, divide the radicand by the biggest perfect square that will go into it evenly

3. Next, simplify the perfect square

***For a radical to be in simplest form, the radicand cannot be divisible by any perfect squares

1.6a_simplifying radicals.notebook October 23, 2014

Ex 8: Simplify. Simplifying Radicals1. First see if the number is a perfect square

2. If it's not a perfect square, divide the radicand by the biggest perfect square that will go into it evenly

3. Next, simplify the perfect square

***For a radical to be in simplest form, the radicand cannot be divisible by any perfect squares

1.6a_simplifying radicals.notebook October 23, 2014

To multiply two radicals that aren't perfect squares, multiply their radicands, then put the square root with the new number. Once you have your new answer, you need to check to see if it can be simplified

To divide two radicals that aren't perfect squares, divide their radicands, then put the square root with the new number. Once you have your new answer, you need to check to see if it can be simplified

1.6a_simplifying radicals.notebook October 23, 2014

Simplify:

Example 12

Example 9Example 10

Example 11