What is the square root of 6 to the nearest integer?

Answer 1

The answer is 2
Without higher level math, this is a little bit tedious. The easiest way to approach the problem is to realize √6 = √3√2 ~= (2)(1) = 2, however, the method to use is as follows:

Let A be some number

A x A = A2 ~= 6

Let A=1: 1 x 1 = 1 < 6

Let A=2: 2 x 2 = 4 < 6

Let A=3: 3 x 3 = 9 > 6

Therefore A must be between 2 and 3, denoted:

2 < x < 3

Test a number in the middle, 2.5:

Let A=2.5: 2.5 x 2.5 = 6.25

6.25 rounds to 6 (and not 7), which means A is closer to 2 than it is to 3.

Therefore √6 ~= 2