1 Answer

The square root of 7 will not be a whole number. You can use a calculator, > Square Root Calculator reduces any square root to simplest radical form and calculates approximation of root or you can use the guessing method.

Guessing Method

Find a whole number square root before the square root of 7 and after.

The square root of 4 is 2.

The square root of 9 is 3.

So, the square root of 7 lies between 2 and 3.

Guess: 

2.5^2  =  6.23   >   too low

2.9^2  =  8.41  >  too high

The square root of 7 is between 2.5 and 2.9

2.7^2  =  7.29  >  too high

2.6^2  =  6.76  >  we'll start here, but still too low

2.65^2  =  7.0225  >  too high

2.64^2  =  6.9696  >  we'll continue here, but still too low

2.649^2  =  7.017201  >  too high

2.646^2  =  7.001316  >  too high

2.645^2  =  6.996025  >  we'll continue here, but still low

2.6455^2  =  6.99867025  >  low

2.6456^2  =  6.99919936  >  low

2.6457^2  =  6.99972849  > we'll continue here, but still low

2.6458^2  =  7.00025764  >  too high

2.64575^2  =  6.9999930625  >  we'll continue here, getting closer

2.64576^2  =  7.0000459776  >  high

2.645755^2  =  7.000019520025  >  high

2.645753^2  =  7.000008937009  >  high

2.645751^2  =  6.999998354001  >  we'll continue here, but I'm going to stop. The calculator will give you the rest. 

I THINK YOU WOULD RATHER USE THE CALCULATOR!