The document discusses square roots and how to estimate them. It defines a square root as a number that, when multiplied by itself, gives the original number. It also defines perfect squares as numbers with whole number square roots and rational numbers as integers, fractions, and perfect squares, while irrational numbers are square roots of non-perfect squares. The document recommends estimating square roots by finding the perfect squares above and below the given number and taking the square roots of those numbers.

1. Section 9.3 Finding and Estimating Square Roots

2. Questions What is a perfect square? Perfect Square: Numbers with square roots that are whole numbers. 1×1 = 1 2×2 = 4 3×3 = 9 4×4 = 16 5×5 = 25 6×6 = 36 7×7 = 49 8×8 = 64 9×9 = 81 10×10 = 100 11×11 = 121 12×12 = 144 15×15 = 225 25×25 = 625

3. Questions What is a square root? Square Roots: A number that, when multiplied by itself, gives the original number. because 9 × 9 = 81

4. Questions About Square Roots: If there is no sign in front of a square root, then the answer should be positive . A − or ± in front of the square root tells the sign.

5. Questions Simplify each expression:

6. Questions What’s the difference between rational and irrational numbers? Rational Numbers: whole numbers fractions terminating or repeating decimals integers 3, 25, 197 0, -4, 17 perfect squares

7. Questions What’s the difference between rational and irrational numbers? Irrational Numbers: non-terminating AND non-repeating decimals square roots of numbers that are NOT perfect squares

8. Questions Tell whether each expression is rational or irrational : irrational irrational rational rational

9. Questions How do you estimate a square root? Estimate Square Roots: Find the perfect square larger and smaller than the given number. Take the square roots. smaller larger between 8 and 9

10. Questions Between what two consecutive integers is each square root? smaller larger between 5 and 6 smaller larger between -11 and -10