The document discusses square roots including: 1. Defining square roots and the radical symbol, and that the square root of a number can be positive or negative. 2. Explaining that the principal square root is always positive and how to identify squares of integers from 1 to 20. 3. Giving examples of simplifying square root expressions and identifying numbers as rational or irrational. 4. Discussing estimating square roots by finding what two consecutive integers a square root lies between.

1. Square Roots Basic Lesson

2. 1. Definition & Terms If a 2 = b, then a is a square root of b 9 2 = 81 and (-9) 2 = 81 so 9 & -9 are both square roots of 81 The radical symbol √ indicates a square root. In Microsoft, the top bar is missing on the radical. You need to draw it. On your calculator, you get √ (

3. 2. Definition & Terms The √ 81 means the positive (principal) square root of 81. The principal square root is the positive square root. - √81 means the negative square root of 81. Memorize squares and square roots from 1 – 20

4. 3. Simplify the expression √ 64 = - √100 = +/- √ 9/16 = +/- √ 0 = √ - 16 =

5. 4. Identify as rational or irrational Rational numbers – Terminate or repeat The square roots of perfect squares Irrational numbers – Continue without repeating Anything that isn’t rational is irrational Make a list of the perfect squares √

6. 5. Identify as rational or irrational √ 8 √ 225 √ 75 √ 1/4

7. 6. Estimating & Using Square Roots The squares of integers are called perfect squares Between what two consecutive integers is √ 15.79? √ 9 < √ 15.79 < √ 16 So it’s between 3 & 4

8. 7. Simplify square roots and round to the nearest hundredth. Use your calculator and don’t forget to use approximately symbol. ≈

9. 8. Word problems A tower is supported with a wire. d = √ x 2 + (2x) 2 gives the length of d of the wire for the tower. Find the length of the wire if x = 12 √ ((12) 2 + (2(12)) 2 ) ≈ 26.83 feet long Try it with x = 140