SOLUTION: Write each of the following square roots in the form a√b where a and b are integers and b has the least value possible. These are all square roots. 360 40 240

Algebra ->  Square-cubic-other-roots -> SOLUTION: Write each of the following square roots in the form a√b where a and b are integers and b has the least value possible. These are all square roots. 360 40 240       Log On


   



Question 411591: Write each of the following square roots in the form a√b where a and b are integers and b has the least value possible.
These are all square roots.
360
40
240



Answer by jjordan95(63) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28360%29
First thing you need to do is a prime factorization of the inside term.
360+=+36%2A10+=+6%2A6%2A10+=+6%2A6%2A2%2A5 I realize that 6 is not a prime number, however, since it comes up an even number of times in the factorization, there is no reason to factor it further. Since 6 came up twice, you can move one outside of the square root sign and cross the other one out. 6sqrt%282%2A5%29 Since there are no other numbers that come up more than once, you are done. highlight%286sqrt%2810%29%29
=======================================
sqrt%2840%29
40+=+10%2A4+=+2+%2A+5+%2A+2+%2A+2
Therefore, you can move 1 of the 2's outside, and cross one of them out.
highlight%282sqrt%2810%29%29
=======================================
sqrt%28240%29
240+=+6%2A+40+=+2+%2A+3+%2A+10+%2A+4+=+2+%2A+3+%2A+2+%2A+5+%2A+2+%2A+2
Therefore you can take two 2's out and cross the other two out.
highlight%284sqrt%2815%29%29