MHB How does \sqrt{300} =10\sqrt{3} when simplified?

[OMGMathPLS]

And does simplify mean the same as solve?Sorry, it should be sq rt sign 300

simplified to 10 sq rt sign 3

 

[Dethrone]

Here, simplify simply means to simplify, not solve. To be more precise, you must simplify the left side so that it equals the right side.
How can you simplify $\sqrt{300}$? Can you possibly rewrite $300$ as a product of two numbers, where one of them is a perfect square? (Wondering)

 

[Jameson]

Hi again,

There is a nice rule that $\sqrt{ab}=\sqrt{a}*\sqrt{b}$. So if we can break the thing inside the square root into two pieces, often times one part of this simplifies. Can you think of how to maybe break down 300?

 

[OMGMathPLS]

Yes, I can, but 3 * 10 is only 30. So it is ^2 ed somehow. But not sure.

 

[Jameson]

Yes, I can, but 3 * 10 is only 30. So it is ^2 ed somehow. But not sure.

I agree that 3*10=30 but we need two numbers that make 300, not 30. Can you think of two numbers that make 300?

 

[kaliprasad]

to evaluate square you need to factor

$300 = 2^2*3*5^2$
now collect all the numbers with even powers separating odd as even + 1

$300= (10)^2 * 3$

to take square root all the things with power 2 shall come once that is 10 and the number with power 1 square need to be taken

so $\sqrt{300} = 10\sqrt{3}$

if it were 200 it would be $200 = 2^3 * 5^2 = 2^2 * 5^2 * 2$ and square root = $10\sqrt{2}$

 

[OMGMathPLS]

Do you really have to break down a square root mentally like that? There's not an easier way like just moving it over and turning a 0 into the 1? You have to just sit there and think of exponent combinations? That could take like 10 minutes for me.

 

[topsquark]

Do you really have to break down a square root mentally like that? There's not an easier way like just moving it over and turning a 0 into the 1? You have to just sit there and think of exponent combinations? That could take like 10 minutes for me.

The more you work with it the easier it becomes. Probably the best advice I can give you is when you have a problem like this, start by trying factors of 1^2, then 2^2, then 3^2, etc. It might take a little while, but if you are on your own you can use a calculator to get started. Eventually you will not need one.

-Dan

 

[Jameson]

It's actually not that bad for smaller numbers. If you just remember basic squares like 4, 16, 25, 36, etc. you can easily spot these. I'm sure you know that $10^2=100$ so whenever you see something a number like 200,300,400, etc. you know that you can break this down into 100 times something.

In your case if you notice that 300 = 100*3 then you are almost done with the problem.

$\sqrt{300}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$.

It really does get easier with practice.

 

[Dethrone]

Not worries, I don't think it is actually necessarily to break it down like that for simple radicals like this one. He was simply demonstrating a technique that can be applied in a general case, especially when you encounter tricky ones.

We have $\sqrt{300}$. We also know that $3 \cdot 100 = 300$, and that $100$ is a perfect square. Thus, $\sqrt{300}=\sqrt{3 \cdot 100}=\sqrt{3 \cdot 10^2}$. Now use what Jameson said above and break the square root in two :D

 

[OMGMathPLS]

Ok, thank you.

So you just find a multiple or something in the sq rt sign and then separate it, throw a sq rt sign back over the left one only?

So like sq rt sign 500 simplified, is going to be 5*100

But then you switch it and move the 5 to the left and put the sq rt over the 100 and remove a 0

I'm sorry.

 

[ineedhelpnow]

Simplifying: bringing it down to the lowest and most basic form.
Solving: finding a final answer

$\sqrt{300}$ is equal to $\sqrt{10*10*3}$. $\sqrt{300}$ is the second root only you leave the two out. in otherwords its the same as $\sqrt[2]{300}$. $\sqrt{100*3}$ which is the same as $sqrt{100}*\sqrt{3}$ and that's $10\sqrt{3}$

 

[Jameson]

Don't think of it as removing a 0 or removing a 1 and don't worry about the order of the two numbers. The order actually doesn't matter since 3*100=100*3=300. You can write it either way.

The thing you need to focus on is taking the square root. Let's try another example. Can you try to simplify this?

$\sqrt{12}=$?

How can you break this down into two numbers, once of which might be "convenient"?

 

[Dethrone]

I think you'll understand if I break it down into steps:

$$\sqrt{300}=\sqrt{3\cdot 10^2}=\sqrt{3}\sqrt{10^2}=\sqrt{3}(10)=10\sqrt{3}$$

 

[OMGMathPLS]

Yes, thanks Rido12, I got it because you said perfect square so it canceled out the sq rt right?sq rt 12 =2 sq rt 3 because there is a ^2 exponent canceled out by the sq rt.

 

[Dethrone]

Precisely! :D

 

[OMGMathPLS]

Oh. Well thanks for the help.

So 3 sq rt 2 and 2 sq rt 3 are two totally different things, right?

Baby steps. smh

 

[ineedhelpnow]

yes the first is 18 and the second is 12

 

[Dethrone]

Yep~

Don't know if you caught my edit, but I misread it at first because of formatting, but you were right with what you wrote :D