Square root help?

Question

my sons book has nothing in the book on how to do this problem, so I can't help him. The problem reads,-Estimate the square root of 180 by finding a natural number "a" such that a< (180 inside square root sign) < a +1

Answer 1

Can you find a number whose square root is a little greater than the square root of 180? How about 196, whose square root is 14?

Can you find a number whose square root is a little less than the square root of 180? How about 169, whose square root is 13?

Since 180 is between 169 and 196, the square root of 180 will also be between the square root of 169 and the square root of 196, namely between 13 and 14.

So estimate 13.5.

Actually, since 180 is closer to the 169 than the 196, the answer would be a little closer to the 13 than the 14, say 13.4

Answer 2

what they are asking you to do is estimate the square root

13^2=169
14^2=196


therefore 13
the root of 180 is somewhere between 13 and 14

Answer 3

a=13