Question 287577
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(18)}}}


Think of the various ways you can reach 18 through multiplication.  There is:

{{{1*18}}}
{{{3*6}}}
{{{2*9}}}


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


{{{5sqrt(18)}}}  <----This can be rewritten as:
{{{5sqrt(2*9)}}}   


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(2)}}}  BUT don't forget the 3 that you got from the {{{sqrt(9)}}}.  You have to multiply that 3 times the 5 that was already sitting outside the sign.


{{{5 * 3 = 15}}} soooo we write the problem as:  {{{15sqrt(2)}}}


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


{{{5sqrt(18)}}}
{{{5sqrt(2*9)}}}
{{{(5*3)sqrt(2)}}}
{{{15sqrt(2)}}}


I hope this helps. :-)