Can someone explain how to get simplified square root answers like what is the square root of 216? and how did you get it?

I don't know................

216 = 36 * 6

√216 = √36 * √6 = 6√6

Find its factors

2( 216

2(108

2)54

3)27

3)9

3)3

= 1

Hence

2^3 x3^3

2^(3/2) x 3^(3/2)

2sqrt(2) x 3sqrt(3)

6sqrt(6)

Separate the number into groups of two, starting at the decimal point. 2 16.

The closest root of 2 without going over is 1, so the first digit is 1. Guess that the next digit is zero.

We have 10 * <something> = 216, so the <something> is 21.6.

Average of 10 and 21.6 is 15.8

We have 15.8 * <something> = 216, so the <something> is 13.6709, and the new average is 14.7354

(need to use lots of pencil and paper to figure that last step).

Just keep continuing like that. There are other manual methods that are faster but more complicated.

Or just use a calculator.

use a calculator

√216 = 14.70 to 4 places