# 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#