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Wheel of Theodorus. How do I determine if a number is rational or irrational? How do I estimate the values of square roots that are irrational? How do I estimate lengths of hypotenuses of right triangles?. Bell Ringers The square root of 17 is between what two consecutive whole numbers?

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## How do I determine if a number is rational or irrational?

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**Wheel of Theodorus**How do I determine if a number is rational or irrational? How do I estimate the values of square roots that are irrational? How do I estimate lengths of hypotenuses of right triangles? Looking for Pythagoras Prob. 4.1**Bell Ringers**• The square root of 17 is between what two consecutive whole numbers? • Estimate the square root of 17 to 1 decimal place. Approximately 4.1 3. 42 = 16, 52 = 25; therefore, the square root of 17 is between 4 and 5. Define rational numbers. Any number that can be written in the form of where b ≠ 0. This includes whole numbers, fractions, & decimals both repeating and terminating.**Standard: M8N1. Students will understand different**representations of numbers including square roots, exponents, and scientific notation. c. Recognize square roots as points and as lengths on a number line. Essential Question: How can we use what we know about right triangles to “plot” the lengths of irrational numbers on a number line?**What is the area of the square above?**Yes, it is 2 sq. cm. What is the length of the side of the square? Yes, it is the square root of 2 which is about 1.4. How long is the square root of 2; where would it “fit” on a number line? We can “copy” that length and mark it on the number line.**How do you think the wheel of Theodorus was created?**How do we determine the length of the first hypotenuse? How do we determine the length of the second hypotenuse? • 2 g**Now, cut out your ruler and transfer the length of**hypotenuse 1 to your ruler.Now, transfer the length of hypotenuse 2 to your ruler. You are placing irrational numbers on a number line…cool!**How can we use what we know about right triangles to**“plot” the lengths of irrational numbers on a number line?

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