Name:
SQUARE ROOTS
Square Roots of Perfect Squares
√4
√25
√1
√9
√16
For √𝑎, √
√
√
√
√
√
√
√
√
is called the radical and 𝒂 is called the radicand.
Two Main Properties for Square Roots
1. Multiplying two square roots is the same as multiplying the radicands then square rooting:
2. Dividing two square roots is the same as dividing the radicands then square rooting:
INSTRUCTIONS
Use property 1 (and maybe property 2) to rewrite each square root so that the radicand is as small as possible.
This is called “simplifying the radical” or “simplest radical form”.
Examples:
1. √200
2. 6√45
3. √75
4. 5√98
12
18
5. √ 9
6. √ 4
7. √2 ∙ √50
8. 4√20 + 7√8
PRACTICE PROBLEM SET
1. Solve for 𝑥 and express your answer in simplest radical form.
Examples:
1. 𝑥 2 − 28 = 0
𝑥 2 = 28
𝑥 = √28
= √4 ∗ 7
= √4 ∗ √7
= 𝟐√𝟕
2. (𝑥 + 5)2 = 72
𝑥 + 5 = √72
𝑥 + 5 = √36 ∗ 2
𝑥 + 5 = 6√2
𝑥 = 𝟔√𝟐 − 𝟓
a. 𝑥 2 − 24 = 0
b. (𝑥 − 7)2 = 50
c. −(𝑥 − 3)2 = −28
d. (𝑥 + 2)2 − 27 = 0
2. Use a graphing calculator to create a table (provided), carefully plot the graph of the function shown below,
and identify its domain and range.
𝑓(𝑥) = √𝑥 + 5 + 2
𝑥
𝑦
Domain: ___ < 𝑥 < ___
Range: ___ < 𝑦 < ___