## 1.2 Learn Basic Properties and Operations

This lesson will help you learn the basic properties and rules that govern math problem-solving.

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

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 $${10^2} = 100$$.