Please help!! Simplify radical expressions.

Question

yanasidlinskiy · Answer

$$\sqrt{75} +\sqrt{3}$$

yanasidlinskiy · Answer

@johnweldon1993 Do you mind helping me??

whpalmer4 · Answer

What is the factorization of 75?  Does it contain any perfect squares?

johnweldon1993 · Answer

Yeah of course :)

Hint* how can you simplify 75? Factorization...

yanasidlinskiy · Answer

No. It doesn't

yanasidlinskiy · Answer

That's the part that I don't get. How do I do that?

johnweldon1993 · Answer

Are you sure?

Remember perfect squares

1, 4, 9, 16, 25, etc ...can 75 be divided by any of those evenly?

yanasidlinskiy · Answer

It can be divided by 5 and you get 13.

johnweldon1993 · Answer

But remember 5 is not a perfect square...

75 CAN however be divided by 25...it goes in 3 times right?

$$\large \sqrt{75} = \sqrt{25 \times 3}$$

Right?

yanasidlinskiy · Answer

Yes.

johnweldon1993 · Answer

Alright....well now lets see...we have

$$\large \sqrt{25 \times 3}$$

What is the square root of 25?

yanasidlinskiy · Answer

5.

johnweldon1993 · Answer

Correct...so we can pull that out of the radical like so:

$$\large 5\sqrt{3}$$

Make sense so far?

yanasidlinskiy · Answer

Yes. It does make sense. Simple and easy when someone explains step by step!:) Keep going.

johnweldon1993 · Answer

Alright perfect...

so now that was just the 75 part of the question....but now we have

$$\large 5\sqrt{3} + \sqrt{3}$$

Right? *just brought the rest of the original question into play

yanasidlinskiy · Answer

Yes.

johnweldon1993 · Answer

Alright...so now remember the rule

$$\large a\sqrt{n} + b\sqrt{n} = (a + b)\sqrt{n}$$

johnweldon1993 · Answer

So if that is true we have

$$\large 5\sqrt{3} + \sqrt{3} = (5 + 1)\sqrt{3} = \space?$$

yanasidlinskiy · Answer

$$6\sqrt{3}$$ ?? I don't know..

johnweldon1993 · Answer

You are correct! what confused you?

yanasidlinskiy · Answer

Umm...well like all those numbers like before the (5+1)

johnweldon1993 · Answer

Oh...okay so think about it like this...

$$\large 5\sqrt{3}$$
^ think about it like...we have 5 copies of √3    okay?

yanasidlinskiy · Answer

Ok.

johnweldon1993 · Answer

And we want to add on

$$\large \sqrt{3}$$

^ and this is 1 more copy of that √3   right?

yanasidlinskiy · Answer

Yes.

johnweldon1993 · Answer

So altogether we have

(5 + 1) copies of that √3

Which indeed is

$$\large 6\sqrt{3}$$

*6 copies of √3

johnweldon1993 · Answer

Did that make it better? :)

yanasidlinskiy · Answer

Yes. It did!!! Thank you so much for your help!!!!

johnweldon1993 · Answer

Anytime :)

whpalmer4 · Answer

as for the $\sqrt{3}+5\sqrt{3}$ business, just think of $\sqrt{3}$ like it is a variable.  You would have no trouble seeing that $a + 5a = 6a$, right?