# What is the square root of 3.4?

##### 1 Answer

#### Explanation:

If

If

So:

#sqrt(3.4) = sqrt(85/25) = sqrt(85)/sqrt(25) = sqrt(85)/5#

Here I have chosen to express

I could also have written

If I wanted to calculate an approximation for

#sqrt(3.4) = sqrt(340/100) = sqrt(340)/10#

Then I would work out an approximation for

For example:

#18 = sqrt(324) < sqrt(340) < sqrt(361) = 19#

Using a Newton Raphson type method to find

#a_(i+1) = (a_i^2 + n)/(2a_i)#

where

Then

#a_1 = (37^2 + 340 * 2^2) / (2 * 37 * 2) = (1369+1360)/148#

#= 2729 / 148 ~~ 18.439#

So