1.6a_simplifying radicals.notebook
1.5a: Simplifying Radicals
October 23, 2014
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:
5
The number in the radical
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
Examples:
1.
81n2
2. 3.
(x+1)
3
8n9
4.
4
m8n4
4
October 23, 2014
1.6a_simplifying radicals.notebook
October 23, 2014
Try These:
1. ­ √121a c
6 2
2.
_+
√169
3. √(8x -2)2
4. √(2x - 7) 6
6
1.6a_simplifying radicals.notebook
October 23, 2014
Simplifying Radicals
1. 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
Ex 5: Simplify.
October 23, 2014
Simplifying Radicals
1. 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
Ex 6: Simplify.
October 23, 2014
Simplifying Radicals
1. 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
Ex 7: Simplify.
October 23, 2014
Simplifying Radicals
1. 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
Ex 8: Simplify.
October 23, 2014
Simplifying Radicals
1. 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
Simplify:
October 23, 2014
Example 10
Example 9
Example 11
Example 12