SOLUTION: What is the square root of 5 on the outside of the check mark and 18 inside the check mark?

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Question 287577: What is the square root of 5 on the outside of the check mark and 18 inside the check mark?
Answer by PRMath(133) About Me  (Show Source):
You can put this solution on YOUR website!
What is the square root of 5 on the outside of the check mark and 18 inside the check mark?

(I love the description of the square root sign as a check mark. That was a great description and let me know immediately what the problem should look like). :-) Excellent. :-)

So ok... here is your problem: 5sqrt%2818%29

Think of the various ways you can reach 18 through multiplication. There is:
1%2A18
3%2A6
2%2A9

Let's look at that 2%2A9 choice. In that situation, you can take the square root of 9, right? In other words, you know what this is: sqrt%289%29. This answer to sqrt%289%29 is 3. Keep that in your mind now and look at your problem this way:

5sqrt%2818%29 <----This can be rewritten as:
5sqrt%282%2A9%29

Now... let's take the square root of 9, which is 3, k? We can "pull" that 3 out of the square root sign and we'll leave the 2 on the inside of the square root sign -- inside the check mark, like this:

5sqrt%282%29 BUT don't forget the 3 that you got from the sqrt%289%29. You have to multiply that 3 times the 5 that was already sitting outside the sign.

5+%2A+3+=+15 soooo we write the problem as: 15sqrt%282%29

So... here it is so you can see it all together:

5sqrt%2818%29
5sqrt%282%2A9%29
%285%2A3%29sqrt%282%29
15sqrt%282%29

I hope this helps. :-)