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Transcript
```Symbols
Defn: a is the positive (or principal) square root of a.
It is the positive number whose square is a.
Every radical expression contains three parts:
index
symbol
3
64
This expression represents the number we must cube to get 64.
Because 43  64 , we say that 3 64  4
NOTE: When an index is not shown, it is assumed to be a 2.
You might want to memorize the first
few square and cube roots?
1 1
4 2
9 3
3
1 1
3
82
3
27  3
3
64  4
3
125  5
16  4
25  5
36  6
49  7
64  8
81  9
100  10
121  11
144  12



The even power of a
real number is always
4
positive or zero. (2)   2 2 2 2  16
Thus, an even root of a
negative number is
4
16 
undefined on the set of
real numbers.
An odd root of a
3
negative number will

8


2
always be negative.
Keep It Straight!
The negative square root
of 9 is -3!
 9  3 Where the square root of
9 
a negative number
is undefined on the set of
real numbers.
Now,You’ve Got It!

easy.
4
4 2


25
25 5
Just take the
square root
of the
numerator AND
take the square
root of the
denominator!
Examples:
 16   4
121  11
4
81  3
3
27  3
0 0
Remember: it is okay to have
a negative radicand if the root
odd.. We just get a NEGATIVE
Rational or Irrational, that is the
question?


out nice and easy..
Others not so nice..
Since there is no
number that raised to
the third power gives
us 12, our calculator
has to approximate it:
 7  7  7  7   7
4
2401 
3
12  2.289428485...
4
If the decimal approximation terminates or repeats it is a rational
number.
If the decimal approximation does not terminate or repeat, it is
called an irrational number.
```
Related documents
The text passage is a transcript or educational material that explains the concept of square roots and cube roots, including how to calculate them and the difference between rational and irrational numbers. It also provides examples and notes on the properties of roots.
no_question

the passage does not contain any explicit mathematical questions or problems for the reader to solve. it is primarily instructional content.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
Survey

* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project

Document related concepts

Positional notation wikipedia , lookup

Location arithmetic wikipedia , lookup

Vincent's theorem wikipedia , lookup

Fundamental theorem of algebra wikipedia , lookup

Elementary mathematics wikipedia , lookup

Transcript
```Symbols
Defn: a is the positive (or principal) square root of a.
It is the positive number whose square is a.
Every radical expression contains three parts:
index
symbol
3
64
This expression represents the number we must cube to get 64.
Because 43  64 , we say that 3 64  4
NOTE: When an index is not shown, it is assumed to be a 2.
You might want to memorize the first
few square and cube roots?
1 1
4 2
9 3
3
1 1
3
82
3
27  3
3
64  4
3
125  5
16  4
25  5
36  6
49  7
64  8
81  9
100  10
121  11
144  12



The even power of a
real number is always
4
positive or zero. (2)   2 2 2 2  16
Thus, an even root of a
negative number is
4
16 
undefined on the set of
real numbers.
An odd root of a
3
negative number will

8


2
always be negative.
Keep It Straight!
The negative square root
of 9 is -3!
 9  3 Where the square root of
9 
a negative number
is undefined on the set of
real numbers.
Now,You’ve Got It!

easy.
4
4 2


25
25 5
Just take the
square root
of the
numerator AND
take the square
root of the
denominator!
Examples:
 16   4
121  11
4
81  3
3
27  3
0 0
Remember: it is okay to have
a negative radicand if the root
odd.. We just get a NEGATIVE
Rational or Irrational, that is the
question?


out nice and easy..
Others not so nice..
Since there is no
number that raised to
the third power gives
us 12, our calculator
has to approximate it:
 7  7  7  7   7
4
2401 
3
12  2.289428485...
4
If the decimal approximation terminates or repeats it is a rational
number.
If the decimal approximation does not terminate or repeat, it is
called an irrational number.
```
Related documents
user
The text passage is a transcript or educational material that explains the concept of square roots and cube roots, including how to calculate them and the difference between rational and irrational numbers. It also provides examples and notes on the properties of roots.

TYPE: NO_QUESTION

The passage does not contain any explicit mathematical questions or problems for the reader to solve. It is primarily instructional content.