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Intro to square roots
Transcript of Intro to square roots
What is a square root?
A number when multiplied by itself gives you a specified number.
It is the opposite or inverse operation of squaring a number.
The symbol for square rooting is √.
√61 is pronounced as “the square root of 61”.
Examples of square roots of perfect squares:
√List of square roots of perfect squares (1-25)
Is the √36 = 18, why or why not?
What is √9? Why?
Technically each positive number has a positive and a negative square root.
This is because a positive times a positive is a positive.
However, a negative times a negative also is a positive.
The positive square root is also called the principal square root.
When there is no ± or – in front of the √, the principal root is usually assumed.
Radical expression: an expression (meaning there is no =) where there is √ , ³√ , etc.
The index is the number in
If there is no index, what you think is implied? What is the name for it?
The radicand is the number in
Let’s figure out what the two consecutive integers √83 is between.
I will use √81. Why did I chose it?
This square root is between this and this number…
I can now say this:
What do you think that means?
What do you think the two consecutive integers are between √81 is between?
This square root is between this and this number…(continued)
Two consecutive integers are two numbers that follow each other.
Can you think of two consecutive integers?
Considering we first chose √81, what do you think the next square root should be?
But what are two consecutive integers?
Hense, √83 is much closer to 9 to as it is to 10. We will now see why this is mathematically true on the next slide.
Let’s look at this on a number line.
So, what is √83 approximately?
Let’s go back to √81 < √83 <√100.
Subtract: 83-81= 2
Subtract again: 100-81=19
Now I divide 2 by 19. It is approximately 0.11.
Remember I said √83 is between the numbers 9 and 10? Therefore,√83 ≈ 9.11. It was also supposed to be much closer to 9 than to 10. It was!
Estimating square roots
Still unsure? Watch this video.