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# Intro to square roots

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## Pamela Skulsky

on 29 June 2013

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#### Transcript of Intro to square roots

Square roots: an introduction
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?

Principal
square roots
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
green
:
³
√8
If there is no index, what you think is implied? What is the name for it?

The radicand is the number in
purple
:
³√
8
Some vocabulary
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:
√81<√83<√100
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.
Full transcript