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1.1 Square Roots and Perfect Squares • For each shaded square: – What is its area? – Write this area as a product. – How can you use a square root to relate the side length and area? Calculate the Area: For the area of each square in the table… • Write the area as a product. • Write the side length as a square root. Squaring vs. Square Rooting • Squaring and square rooting are opposite, or inverse operations. – Eg. 9 = 9= 2 • When you take the square root of some fractions you will get a terminating decimal. – Eg. 225 = 100 • When you take the square root of other fractions you will get a repeating decimal. – Eg. 1 9 = = = • These are all called _________________________ Assignment • Page 11-12 • Questions 3-14 1.2 Square Roots of NonPerfect Squares Introduction... • Many fractions and decimals are __________________________________ • A fraction or decimal that is not a perfect square is called a ___________________ – The square roots of these numbers do not work out evenly! • How can we estimate a square root of a decimal that is a nonperfect square? Here are 2 strategies... Ask yourself: “Which 2 perfect squares are closest to 7.5?” 7.5 7.5 Strategy #2... Use a calculator! Example #1 • Determine an approximate value of each square root. 8 5 close to 9 close to 4 Example #2 • Determine an approximate value of each square root. Your benchmarks! 3 10 3 B 10 What’s the number? • Identify a decimal that has a square root between 10 and 11. Mr. Pythagoras • Junior High Math Applet Practicing the Pythagorean Theorem First, ESTIMATE each missing side and then CHECK using your calculator. 7 cm x 5 cm 8 cm 13 cm x Applying the Pythagorean Theorem 1.5 cm 2.2 cm 6.5 cm The sloping face of this ramp needs to be covered with Astroturf. a) Estimate the length of the ramp to the nearest 10th of a metre b) Use a calculator to check your answer. c) Calculate the area of Astroturf needed. Let’s quickly review what we’ve learned today... • Explain the term non-perfect square. • Name 3 perfect squares and 3 nonperfect squares between the numbers 0 and 10. • Why might the square root shown on a calculator be an approximation? Assignment Time! • page 18 -20 • Questions 1- 20