1.2 Learn Basic Properties and Operations

Without a calculator, the exact square root of a number may difficult to find. However, you can find the approximate square root of a number by thinking of the square numbers closest to your number. For example, you know that the square root of 12 must be between 3 and 4 because 12 falls between $${3^2} = 9$$ and $${4^2} = 16$$.

Example

Which of the following is the best estimate for the square root of 70?

A. between 7 and 8
B. between 8 and 9
C. between 9 and 10
D. between 30 and 40

Answer
The number 70 is greater than $${8^2} = 64$$ and less than $${9^2} = 81$$, so the correct choice is B. Using a calculator, we see that the square root of 70 is about 8.37.

A represents the range of numbers from $${7^2} = 49$$ to $${8^2} = 64$$.

C represents the range of numbers from $${9^2} = 81$$ to $${10^2} = 100$$.

D represents the range of numbers from 900 to 1,600. If you chose D, you may have divided 70 by 2. You need to think, “What number multiplied by itself is 70?”