Square Root vocab. And Square Root Notes

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Monday 5/5

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 · 3 =9 Or -3 · -3 =9 factor factor factor factor

You can write the root as ± 3Principal root is always the Positive root (factor) What is the principal root of 9?

3Index tells you how many of the same factors equals the radicand.Ex: 1 How many factors do we need to multiply to get the radicand?

4 · 4 or -4 · -4 ± 4Ex: 2 How many factors do we need to multiply to get the radicand?

2 · 2 · 2 · 2 ±2

2 164 16

2 9

Variables always have a positive root because you don’t know if the variable represents a pos. or neg. #.

Ex: 2 = h · h so the answer is hExponent rule: When bases are the same and you are multiplying you add the exponents.

Ex: b2 · b2 = b2 + 2 = b4

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: 8 = d4 · d4 = d4 + 4 = d8

factor factor

h

d

Example 1• Find the two square

roots.

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

225

15

Example 2• What is the principal

root of this expression? 14

exponent rule = d7 • d7 = d7 + 7= d14

11d7 · 11d7 factor factor

Solution

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.

d12122 121d

11d7

Example 3• 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 • 9 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.

A

Side = 9 ft

81

flag