1. Square Root vocab. And Square Root Notes absent copy Monday 5/5

2. Index Radical = Grouping Symbol Radicand = Term inside A Root is one of the factors of the radicand. What are two of the same roots (factors) that equals 9 (radicand) when you multiply? · 3 =9 Or · = factor factor factor factor You can write the root as ± 3 Principal root is always the Positive root (factor) What is the principal root of 9? Index tells you how many of the same factors equals the radicand. Ex: How many factors do we need to multiply to get the radicand? · or · ± 4 Ex: How many factors do we need to multiply to get the radicand? · 2 · 2 · ±2

3. Variables always have a positive root because you don’t know if the variable represents a pos. or neg. #. Ex: = h · h so the answer is h Exponent rule: When bases are the same and you are multiplying you add the exponents. Ex: b2 · b2 = b2 + 2 = b When exponents are inside the radical sign find the same 2 factors of the exponent so when you add them they equal the exponent Ex: = d · d = d4 + 4 = d8 factor factor

4. Example 1 15 Find the two square roots. 15 · 15 factor factor
15 · 15
factor factor
-15 · -15
factor factor
What is the radicand?
A radicand is the term inside of the radical sign. 225
What 2 factors (the same) can we multiply to equal the radicand? (Hint there are 2 sets of factors)
The 2 same factors are 15 and 15 or
-15 and -15.
What is the best way to write down the solution?
The best way to write down the solution is to write it like:
± 15 15

5. Example 2 11d7 What is the principal root of this expression? 14
exponent rule = d7 • d7 = d7 + 7= d14
11d7 · 11d7
factor factor
Solution
What is the radicand?
The radicand is 121d14
What is the index and what does it mean? 2
The index tell us how many factors = the radicand. 2 factors
What is the exponent rule we can use to factor the 14?
When bases are the same and we are multiplying we can add the exponents.
What 2 factors (the same) can we multiply to equal the radicand?
11d7 · 11d7
What does principal root mean?
Principal root is always the positive factor.
11d7

6. Example 3 Side = 9 ft (hint s = ) 9 • 9 9 ft factor factor 9 ft
If the flag of Switzerland has an area of 81 ft2, what is the length of each of its sides? The flag is square.
(hint s = )
9 • ft
factor factor 9 ft
Solution
What is the radicand?
The radicand is the area of the flag which is 81.
Do we only find the principal root?
YES or NO
You can only have positive lengths.
What 2 factors (the same) can we multiply to equal the radicand?
The 2 factor that make up 81 are 9 and 9.
What is the length of each side?
The length of each side is 9 ft.
flag
Side = 9 ft