Rational vs. Irrational, Roots, Estimating, and Pythagorean Theorem

Rational vs. Irrational

100

3/4 is an example of a rational number. True or False.

True. It's a fraction.

200

Pi is an example of a rational number. True or False.

False. Pi is irrational.

300

5.75 is an irrational number. True or False

False. The decimal terminates or stops, so it's rational.

400

8.333333333 (where the 3 repeats) is a irrational number. True or False.

False. Since it repeats, it is a rational number.

500

18.897657... is a rational number. True or False

False. The decimal continues on forever.

Roots

100

What is the square root of 81?

9

200

What is the square root of 225?

15

300

What is the square root of 81 + the square root of 25? Hint: Solve for both square roots and then add them together.

14

400

What is the cube root of 27?

3 because 3 x 3 x 3 = 9 x 3 = 27

500

What 2 integers is the square root of 12 in between?

a) 1 and 2

b) 2 and 3

c) 3 and 4

d) 4 and 5

c) 3 and 4. The square root of 9 is 3 and the square root of 16 is 4. 12 is in between 9 and 16.

Pythagorean Theorem 1

100

A right triangle has a leg of 3 and another leg of 4. What is the hypotenuse?

5

200

A right triangle has a height of 12 cm and a base of 10 cm. What is the length of the hypotenuse? Round your answer to the nearest tenth.

15.6 cm

300

A right triangle has a leg that's 8 meters and another leg that is 8 meters. What is the length of the hypotenuse? Round your answer to the nearest tenth.

11.3 meters

400

A triangle has a height of 8 cm, a base of 6 cm, and a hypotenuse of 10 cm. Is this a right triangle? Why or why not?

Yes because the sum of the squares of the legs are equal to the square of the hypotenuse.

500

A construction worker is 10 feet away for the building. The building is 20 feet tall. Approximately how long does the ladder need to be to reach the top of the building in order to fix the siding? 

22.4 feet

Pythagorean Theorem 2

100

A right triangle has a base of 8 cm and a hypotenuse of 10 cm. What is the length of the missing leg?

6 cm

200

A right triangle has a base of 14 cm and a hypotenuse of 16 cm. What is the length of the missing leg? Round your answer to the nearest tenth.

7.7 cm

300

A right triangle has a base of 9 cm and a hypotenuse of 22 cm. What is the length of the missing leg? Round your answer to the nearest whole number.

20 cm

400

A right triangle has a base of 4 cm and a hypotenuse of 7 cm. What is the length of the missing leg? Round your answer to the nearest tenth.

5.7 cm

500

A triangle has a height of 5 cm, a base of 10 cm, and a hypotenuse of 15 cm. Is this a right triangle? Why or why not?

No because the sum of the squares of the legs are not equal to the square of the hypotenuse.

Random

100

What is the slant called in the Pythagorean Theorem?

Hypotenuse

200

When a number can be written as a fraction, is it a rational number or an irrational number?

Rational

300

In the Pythagorean Theorem, what are "a" and "b" called?

Legs

400

The Pythagorean Theorem can be used to find the missing side lengths of any triangle. True or False.

False. ONLY RIGHT TRIANGLES.

500

What's the formula for finding a missing side length in a right triangle?

a² + b² = c²