Warm-up Problems
Simplify the following:
1. (6v2 + 2v – 5) + (3v – 4v2 +7) =
2. - 4v2 (v + 1) =
3. (4n2 + 1) - (2n2 + 6n - 3) =
4. (5n+1)(n−3) =
5. (3a+2)(5a2 −a+1) =
Warm-up Problems
Solutions:
1. 2v2 + 5v + 2
2. - 4v3 – 4v2
3. 2n2 - 6n + 4
4. 15n2 - 14n – 3
5. 15a3 + 7a2 + a + 2
Irrational Numbers
We write “irrational numbers” using a “radical symbol,” often just referred to as a “radical.”
√3 is an irrational number.
√ is the radical sign / symbol, and 3 is called the radicand.
In the expression , is the radical sign and
64 is the radicand.
If x2 = y then x is a square root of y.
1. Find the square root:8
2. Find the square root:-0.2
64
64
0.04
3. Find the square root: 11, -11
4. Find the square root:21
5. Find the square root:
121
441
25
815
9
6. Use a calculator to find each square root. Round the decimal
answer to the nearest hundredth.
6.82, -6.82
46.5
What numbers are perfect squares?1 • 1 = 12 • 2 = 43 • 3 = 9
4 • 4 = 165 • 5 = 256 • 6 = 36
49, 64, 81, 100, 121, 144, ...
How do you simplify variables in the radical?
Look at these examples and try to find the pattern… x7
1x x2x x3x x x4 2x x5 2x x x6 3x x
What is the answer to ? x7
7 3x x x
As a general rule, divide the exponent by two. The remainder stays in the
radical.
Adding & Subtracting Radicals
• The rules for adding and subtracting radicals are very similar to the rules for adding and subtracting polynomials.
• The radical / radicand have to match exactly in order to add or subtract.
IMPORTANT
• If each radical in a radical expression is not in simplest form, simplify them first.
• Then use the distributive property, whenever possible, to further simplify the expression.