How to know that the square root of 13 is not equal to 5.7 without using a calculator

Question

suppose a friend tells you that √13≈5.7 Without a calculator how can you convince your friend that he or she must have made an error.

Answer 1

5.7  times 5.7 is between 5 times 5, which is 25, and 6 times 6, which is 36.  Both of these are much larger than 13.

Sq rt of thirteen is between the sq rt of 9, which is 3, and the sq rt of 16, which is 4.