How do you find the square root of 270?
3 Answers
See the solution process below:
Explanation:
We can use this rule of radicals to rewrite this expression:
If necessary, the
And therefore:
A =
Explanation:
Find a
=
Then find the quotient of the number and the divisor (
= 270 /
= 3
= 3 *
Explanation:
First note that
Next note that if
#sqrt(ab) = sqrt(a)sqrt(b)#
[[ The same is not true if both
Also, if
#sqrt(a^2) = a#
So we find:
#sqrt(270) = sqrt(9*30) = sqrt(9)sqrt(30) = 3sqrt(30)#
This is the simplest form of the principal square root.
We can calculate approximations to
#sqrt(30) = [5;bar(2,10)] = 5+1/(2+1/(10+1/(2+1/(10+1/(2+1/(10+...))))))#
[[ In general
We can get decent approximations for
#sqrt(30) ~~ 5+1/2 = 11/2#
#sqrt(30) ~~ 5+1/(2+1/(10+1/2)) = 241/44#
#sqrt(30) ~~ 5+1/(2+1/(10+1/(2+1/(10+1/2)))) = 5291/966#
Let's stop there and use this to give us an approximation for
#sqrt(270) = 3sqrt(30) ~~ 3*5291/966 = 15873/966 ~~ 16.431677#