Question

I understand absolutely nothing about square roots...help!
What is the exact value of the expressions the square root of 180. − the square root 125. + the square root of 5.? Simplify if possible.
2the square root of 2.
12the square root of 2.
2the square root of 5.
12the square root of 5.

Answer 1

the square root operator is the inverse of the power operator.

Given y=x^2, the inverse is x=Sqrt(y).

Given y=25, the inverse is Sqrt(25), or 5.

Answer 2

What is the square root of 180?

We need to factor 180. To do this, we look for the LARGEST PERFECT SQUARE that divides into 180 with no remainder. To do this, list perfect squares: 1, 4, 16, 25, 36, 49, 81, and so on. Which of these divides into 180 with no remainder? Show 180 in factored form.

Answer 3

i dont know what that means...

Answer 4

Divide 4 into 180.
Divide 9 into 180.
Divide 16 into 180.
And so on.
Which of these perfect squares divides into 180 with no remainder?

Answer 5

9?

Answer 6

\[\frac{ 180 }{ 9 }=\frac{ 90*2 }{ 9 }=\frac{ 9*10*2 }{ 9 }\]

Answer 7

=20, with no remainder. Yes.

Answer 8

So, your 180 factors into 9*20.

Unfortunately, we 're not done yet, since 20 factors into 4*5, and 4 is a perfect square. Can you now reduce 180=9*20=9*(FACTORS OF 20)?

Answer 9

what does that mean?

Answer 10

Let's put it a different way. Determine the factors of 20.

Answer 11

Which two numbers, multiplied together, result in your obtaining 20?

Answer 12

2 and 10, 4 and 5 and 1 and 20

Answer 13

Very good. Now, which of these is a perfect square? {2, 10, 4, 5}

Answer 14

4?

Answer 15

Yes. So, your 9*10*20 becomes 9*10*4*5.
Note that 9*4=36, a perfect square.
So, 180=36* ( ? )

Answer 16

This discussion is needlessly complicated. Sorry.

But it does help to practice factoring, identifying perfect squares, and so on.

Answer 17

5

Answer 18

Right. So, what are all the factors of 180? First list those that are perfect squares, and then list those that are not perfect squares.

Answer 19

i dont know which re perfect squares

Answer 20

i think the answer is c but idk how to justify that

Answer 21

{1, 2, 3, .... ? }

Perfect squares include {1, 4, 9, 16, 25, 36, 49, 64, 81, 100, and so on.}

Earlier I typed the following to you:

Yes. So, your 9*10*20 becomes 9*10*4*5.
Note that 9*4=36, a perfect square.
So, 180=36* ( ? )

You responded (later) with 5.
Thus, 180=36*5. Note that 36 is a perfect square (it comes from 9*9 or 9^2), and that 36 is also the LARGEST perfect square that will divide into 180.

Answer 22

You are supposed to find the exact square root of 180 in this problem.

Answer 23

Since 180 = 36 * 5,

\[\sqrt{180}=\sqrt{36}*\sqrt{5}\]

Answer 24

Find the sqrt of 36. \[\sqrt{36}=?\]

Answer 25

is 6?

Answer 26

Yes. So,\[\sqrt{180}=\sqrt{36}*\sqrt{5}=6\sqrt{5}\]

Answer 27

Next one is 125. What is the exact square toot of 125?

I ask you to do the same thing as before. Find the largest perfect square factor of 125. Hint: It's one of these; {9, 16, 25, 49}.

Answer 28

25?

Answer 29

Harley? I need your attention.

Answer 30

yes

Answer 31

?

Answer 32

What is the square root (exact square root) of 125?
Again I ask you to find the largest perfect square factor of 125. I gave you a list from which to choose. See above.

Answer 33

so its not 25?

Answer 34

It is indeed 25. What's the other factor of 125?

Answer 35

5

Answer 36

Cool. Then,\[\sqrt{125}=\sqrt{25}\sqrt{5}\]

Answer 37

Re-write this in simplest form. That means finding the square root of 25.

\[\sqrt{125}=( ? )\sqrt{\sqrt{5}}\]

Answer 38

also 5?

Answer 39

\[\sqrt{125}=5\sqrt{5}\]

Answer 40

is all you need.

Answer 41

what answer choice would it be though?

Answer 42

I've just reviewed your original posting. You are to write a mathematical expression for "180. − the square root 125. + the square root of 5. You already know that Sqrt(180)=6Sqrt(5), and you know the Sqrt of 125.

Write out the 3 terms in that order.

I'm sorry, but I need to get off the 'Net. I'd be happy to continue working with you later today. Thanks for your hard work and patience.

Answer 43

okay thank you so much