6 8 c When we do Pythagorean Theorem problems, we need to be able to deal with SQUARE ROOTS.

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Presentation transcript:

6 8 c When we do Pythagorean Theorem problems, we need to be able to deal with SQUARE ROOTS

So what is a SQUARE ROOT?

SQUARE ROOTS

This isn’t exactly true, but for the next 2 weeks: “Radical” means the same thing as “square root” *Side Note:

What is a square root?

A square root is a way of asking: “What number, times itself gives this value?”

What is a square root? A square root is a way of asking: “What number, times itself gives this value?” “What number times itself is 25?”

What is a square root? A square root is a way of asking: “What number, times itself gives this value?” “What number times itself is 25?” “5 times 5 is 25.”

“What number times itself is 25?” “5 times 5 is 25.” * This is called “taking the square root.” * Notice, after we have taken the square root, the symbol is gone.

These are the numbers that have a “nice” answer when we take a square root:

What number times itself is 1? These are the numbers that have a “nice” answer when we take a square root:

What number times itself is 4? These are the numbers that have a “nice” answer when we take a square root:

What number times itself is 9? These are the numbers that have a “nice” answer when we take a square root:

What number times itself is 16? These are the numbers that have a “nice” answer when we take a square root:

What number times itself is 25? These are the numbers that have a “nice” answer when we take a square root:

What number times itself is 36? These are the numbers that have a “nice” answer when we take a square root:

Since these numbers give nice answers, we call them perfect squares. 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144

Since these numbers give nice answers, we call them perfect squares. 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144

Since these numbers give nice answers, we call them perfect squares. 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 You will have to know these numbers.

Since these numbers give nice answers, we call them perfect squares. 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 You will have to know these numbers. Do I have to memorize them?

Since these numbers give nice answers, we call them perfect squares. 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 You will have to know these numbers. Do I have to memorize them? You can, but… It is probably easier to just remember how we get them: You can, but… It is probably easier to just remember how we get them:

Since these numbers give nice answers, we call them perfect squares. 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 You will have to know these numbers. Do I have to memorize them? You can, but… It is probably easier to just remember how we get them: You can, but… It is probably easier to just remember how we get them: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, Just square the numbers 1-12.

So, if you have a problem that looks like this:

Just write the number that answers the question:

So, if you have a problem that looks like this: Just write the number that answers the question: “What number times itself is 16?”

So, if you have a problem that looks like this: Just write the number that answers the question: “What number times itself is 16?” 4

The hard part is when the answer is not obvious:

No nice number times itself is 20.

The hard part is when the answer is not obvious: No nice number times itself is 20. There are two options for how to find the square root of 20.

The hard part is when the answer is not obvious: No nice number times itself is 20. Option 1Get an approximate answer (decimal) You just type it in the calculator. (easy) There are two options for how to find the square root of 20.

The hard part is when the answer is not obvious: No nice number times itself is 20. Option 1Get an approximate answer (decimal) You just type it in the calculator. (easy) Option 2 The exact answer. This is like reducing a fraction (hard) There are two options for how to find the square root of 20.

The hard part is when the answer is not obvious: No nice number times itself is 20. Option 1Get an approximate answer (decimal) You just type it in the calculator. (easy) Option 2 The exact answer. This is like reducing a fraction (hard) There are two options for how to find the square root of 20. You will have to be able to do BOTH.

Option 1Get an approximate answer (decimal) You just type it in the calculator. (easy)

Use the square root button here to just type it in the calculator.

Option 1Get an approximate answer (decimal) You just type it in the calculator. (easy) Use the square root button here to just type it in the calculator. Did you get 400? Make sure to hit the “ctrl” key first!

Option 1Get an approximate answer (decimal) You just type it in the calculator. (easy) Use the square root button here to just type it in the calculator. Did you get 400? Make sure to hit the “ctrl” key first!

Option 1Get an approximate answer (decimal) You just type it in the calculator. (easy) This isn’t the best answer, because the calculator had to round the answer.

Option 1Get an approximate answer (decimal) You just type it in the calculator. (easy) This isn’t the best answer, because the calculator had to round the answer. That’s why we call it “approximate” That’s why we call it “approximate”