How do you simplify sqrt216?
1 Answer
Explanation:
The quick version is:
sqrt(216) = sqrt(6^2*6) = 6sqrt(6)
How do we find out that
One way is to split off prime factors one at a time, then recombine them.
Here's a factor tree for
color(white)(0000)216
color(white)(0000)"/"color(white)(0)"\"
color(white)(000)2color(white)(00)108
color(white)(000000)"/"color(white)(0)"\"
color(white)(00000)2color(white)(00)54
color(white)(0000000)"/"color(white)(00)"\"
color(white)(000000)2color(white)(000)27
color(white)(000000000)"/"color(white)(00)"\"
color(white)(00000000)3color(white)(0000)9
color(white)(000000000000)"/"color(white)(0)"\"
color(white)(00000000000)3color(white)(000)3
So we find:
216 = 2*2*2*3*3*3=(2*3*2*3)*(2*3) = 6^2*6
By definition:
sqrt(6^2) = 6
For any positive numbers
sqrt(ab) = sqrt(a)sqrt(b)
Hence:
sqrt(216) = sqrt(6^2*6) = sqrt(6^2)sqrt(6) = 6sqrt(6)
