Examples:
Estimate the squares of some decimals...
3.2*2 (3.2 squared) = 3*2 = 9 and 4*2 is 16 so the answer will be between 9 and 16, but much closer to 9 since 3.2 is much closer to 3...so maybe close to 11?
on a calculator, 3.2 squared is 10.24, so close to the estimate:)
6.8*2 is 6*2 = 36 and 7*2 is 49 so 6.8 *2 is going to be somewhere close to the top end of that range...like 45, 46, 47.
On a calculator, it is 46.24!, or 46.
and
Estimate the square roots...
Just for fun, let's look at squaring Fractions!
Just like regular integers, we can square fractions by writing it out in expanded form...
(1/2)*2 is = 1/2 x 1/2
so the short of it, is since the exponent is touching (or exponenting) the bracket, each piece/number gets the exponent.
(2/3)*2 means both the top 2 and the bottom 3 get squared, and it stay a fraction...
with 4 on the top, and 9 on the bottom.