Eureka Math Grade 8 Module 7 Review

Rational or Irrational?

100

Is the sqrt (7) a rational or irrational number?

Irrational

200

Is 1/sqrt(25) rational or irrational?

Rational

300

True or False: All infinite decimals are rational numbers. If the statement is false, correct the statement.

False. Infinite decimals with repeating patterns are rational numbers. 

400

Is 0.36363636.... rational or irrational?

Rational

500

Determine whether each given number is rational or irrational:

-3.345

Cube root of 125

sqrt(28)

0.81818181.....

3/17

-3.345: Rational

Cube root of 125: Rational

sqrt(28): Irrational

0.81818181....: Rational

3/17: Rational

Square Roots and Cube Roots

100

What is the positive square root of 64?

8 

200

What is the cube root of 27?

3

300

What whole number number is closest to the sqrt(85)?

9

400

What is the sqrt(89) to the nearest tenth?

9.4

500

Which number is bigger? Sqrt(64) or the cube root of 64?

 The sqrt(64)

Pythagorean Theorem

100

What is the formula for the Pythagorean Theorem? State what each variable represents.

a²+b²=c². The variables a and b are the legs of the right triangle and the variable c represents the hypotenuse of the right triangle.

200

The length of the hypotenuse of a right triangle is 15 in and the length of one of the legs is 9 in. Find the length of the other leg of the triangle.

12 in

300

Calculate the  EXACT perpendicular height of an equilateral triangle with side lengths of 4 cm. HINT: leave your answer as a square root.

sqrt(12) cm

400

What is the EXACT distance between the points (-7,7) and (-3,2) on the xy-coordindate plane? HINT: Leave your answer inside the square root.

sqrt(41)

500

What is the length of the diagonal of a rectangular prism with a length of 12 in, width of 5 in, and height of 6 in? HINT: Round your answer to the nearest thousandth. 

14.318 in

Volume

100

How do you find the radius if you are given the diameter?

Divide the diameter by 2.

200

What is the volume of a cone with a radius of 3 cm and a height of 6 cm? Use 3.14 for pi.

V = 56.52 cm³

300

What is the approximate volume of a cone with a radius of 4 cm and a height of 7 cm? Round your answer to the nearest tenth? 

117.2 cm³

400

What is the approximate volume of a sphere with a radius of 3 ft? Use 3.14 for pi.

113.04 ft³

500

Compute the height (in meters) of a cylinder with a radius of 2m and volume 138 cubic meters. Round to the nearest meter. (Use pi = 3.14) 

Height = 11 meters

???Mystery???

100

What is the decimal equivalent of 7/9?

0.777777......

200

What is the decimal equivalent of 5/11?

0.4545454545.....

300

What would be the first step in solving the following equation? 

x² = 49

Take the square root of both sides of the equation.

400

Solve the following equation for x: x³ = 216

x = 6

500

Solve the following equation for x:

x³+3x = 3(x+9)

x = 3