1.1 Square Roots of Perfect Squares Math 90. For each shaded square: –What is its area? –Write this area as a product. –How can you use a square root.

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Presentation transcript:

1.1 Square Roots of Perfect Squares Math 90

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:

Calculate the side length

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. When you take the square root of some fractions you will get a terminating decimal. –Eg. These are all called RATIONAL numbers.

When you take the square root of other fractions you will get a repeating decimal. –Eg. These are all called RATIONAL numbers

1.2 Square Roots of Non-Perfect Squares d

Introduction... Many fractions and decimals are not perfect squares. A fraction or decimal that is not a perfect square is called a non-perfect square. –The square roots of these numbers do not work out evenly! How can we estimate a square root of a decimal that is a non-perfect square?

Here are 2 strategies Ask yourself: “Which 2 perfect squares are closest to 7.5?” is closer to 9 than to 4, sois closer to 3 than to 2. What would be a good approximation?

Strategy #2... Use a calculator! But, of course, you must be able to do both!

Example #1 Determine an approximate value of each square root. close to 9 close to 4 What does this mean? We call these 2 numbers ‘benchmarks’.

Example #2 Determine an approximate value of each square root Of course, you can always use a calculator to CHECK your answer! Your benchmarks!

What’s the number? Identify a decimal that has a square root between 10 and If these are the square roots, where do we start?

Mr. Pythagoras Junior High Math Applet Remember, we can only use Pythagorean Theorem on RIGHT angle triangles!

Practicing the Pythagorean Theorem 5 cm First, ESTIMATE each missing side and then CHECK using your calculator. 8 cm 13 cm 7 cm x x

Applying the Pythagorean Theorem The sloping face of this ramp needs to be covered with Astroturf. a)Estimate the length of the ramp to the nearest 10 th of a metre b)Use a calculator to check your answer. c)Calculate the area of Astroturf needed. 2.2 cm 6.5 cm 1.5 cm

Let’s quickly review what we’ve learned today... Explain the term non-perfect square. Name 3 perfect squares and 3 non- perfect squares between the numbers 0 and 10. Why might the square root shown on a calculator be an approximation?

Assignment Time! Complete the following questions in your notebook. Be prepared to discuss your answers in class. Show all of your work!