1. Square Roots

2. Perfect Squares Squaring is when a number is multiplied by itself – It’s called squared because the area of a square is multiplying a side by itself since all sides are equal A perfect square is the result of squaring an integer – Remember that an integer includes negative numbers, zero and positive numbers – Decimals and fractions are not integers

3. Examples Determine if the given number is a perfect square

4. Square Roots A square root of a number is one of its two equal factors – Think of finding the square root as the opposite of squaring a number Remember the rules of multiplying integers – A positive times a positive is positive – A negative times a negative is positive – A positive times a negative is negative This means that every square root has both a positive and negative answer – The symbol ± is used to show this

5. Simplifying Square Roots Use multiplication facts or calculator to determine the positive square root of a number Sometimes, the problem will specify if it wants the positive or negative square root – If the sign is not specified, you must include the ± sign Since multiplying a number by itself will always give a positive, you CANNOT simplify a negative number – When a problem is asking for the square root of a negative number, the answer is “No real solution”

6. Examples Simplify

7. Irrational Numbers When finding the square root of a number that is not a perfect square, the result will be irrational – Remember, an irrational number cannot be written as a fraction For now, we must estimate where the square root of a non-perfect square will be – What two integers will the result be in between?

8. Estimating a Square Root 1.Check to see if the calculator result is an integer or irrational number -Looking for decimal or no decimal 2.If it is a decimal, use the number in the ones place as a guide to estimate -The next integer will be where it is in between 3.Remember to be mindful of the signs

9. Examples Estimate the square root