Pythagorean Theorem and Rational Numbers

In this episode, Mr. Baskin covers various math problems, focusing on the Pythagorean theorem, solving triangle problems on a grid, and proving the Pythagorean identity without calculations. The lesson also includes identifying numbers between consecutive integers, examples of rational and irrational numbers, and working with powers of 10. The session concludes with a practical problem involving a system of equations to determine the amount of ribbon needed for a school event.

What is the length of the hypotenuse of a right triangle with legs of 2 and 6?

• 8

• 12

• √40

• 10

If a right triangle has legs of 6 and 8, what is the length of the hypotenuse?

• 14

• 10

• 12

• √100

What is the length of the hypotenuse of a right triangle with legs of 3 and 1 on a grid?

• √10

• 4

• 5

• 3

How do you find the length of the hypotenuse of a right triangle with legs of 3 and 4?

• 6

• √25

• 5

• 7

Without calculations, why does 5² + 12² equal 13²?

• Because 13 is a prime number

• Because 5² + 12² forms a square

• Because of the Pythagorean theorem

• Because 5 + 12 = 13

Between which two integers does the square root of 10 lie?

• 2 and 3

• 4 and 5

• 5 and 6

• 3 and 4

Which of the following is an example of a rational number?

• √8

• π

• √2

• 2/3

Which of the following is an irrational number?

• √9

• 4

• √10

• 1/2

How much blue ribbon does Andre need if he requires 50% more blue than green and an extra 6.5 meters?

• 50.25 meters

• 17.5 meters

• 32.75 meters

• 26.25 meters

What is the total length of green ribbon Andre needs?

• 26.25 meters

• 32.75 meters

• 17.5 meters

• 50.25 meters