8th Grade Math Review

Which of the following is NOT a perfect square?

• 1

• 4

• 100

• 8

Answer explanation

A perfect square is an integer that is the square of another integer. The numbers 1 (1x1), 4 (2x2), and 100 (10x10) are perfect squares, while 8 cannot be expressed as the square of an integer, making it NOT a perfect square.

In between what two integers is the square root of 44?

• 3 and 4

• 4 and 5

• 5 and 6

• 6 and 7

Answer explanation

The square root of 44 is approximately 6.63. Since 6.63 is greater than 6 and less than 7, the correct answer is between 6 and 7.

The area of a square is 36 cm².  What is the length of one side?

• 6 cm

• 24 cm

• 9 cm

• 9 cm

Answer explanation

The area of a square is calculated as side length squared. Given the area is 36 cm², we find the side length by taking the square root: √36 = 6 cm. Thus, the length of one side is 6 cm.

The volume of a square is 216 cm³.  What is the length of one side?

• 6 cm

• 26 cm

• 72 cm

• 108 cm

Answer explanation

To find the length of one side of a cube with volume 216 cm³, use the formula V = s³. Thus, s = ∛216 = 6 cm. Therefore, the length of one side is 6 cm.

Change from standard form to scientific notation: 12,000,000

• 12.0  x  10⁷

• 0.12  x  10⁷

• 1.2  x  10⁶

• 1.2  x  10⁷

Answer explanation

To convert 12,000,000 to scientific notation, move the decimal point 7 places to the left, resulting in 1.2. Thus, it is expressed as 1.2 x 10^7, making the correct answer 1.2 x 10⁷.

π or PI is classified as which?

• Rational

• Irrational

• Rational, Real

• Irrational, Real

Answer explanation

π (pi) is classified as an irrational number because it cannot be expressed as a fraction of two integers. It is also a real number, as it exists on the number line. Therefore, the correct classification is 'Irrational, Real'.

4x + 7 = 23

• x = 16

• x = 4

• x = 9

• x = 12

Answer explanation

To solve for x, subtract 7 from both sides: 4x = 16. Then, divide by 4: x = 4. Thus, the correct answer is x = 4.

20 = 2 - a

• a= 18

• a= -18

• a= -10

• a= 12

Answer explanation

To solve for a, rearrange the equation: a = 2 - 20. This simplifies to a = -18. Thus, the correct answer is a = -18.

5( 2x + 3) = ?

• 10x + 3

• 7x + 8

• 10x + 15

• 25x

Answer explanation

To simplify 5(2x + 3), distribute 5: 5 * 2x + 5 * 3 = 10x + 15. Thus, the correct answer is 10x + 15.

-4 ( x + 3) = ?

• -4x + 3

• -4x + 12

• -4x – 12

Answer explanation

To simplify -4(x + 3), distribute -4: -4*x - 4*3 = -4x - 12. Thus, the correct answer is -4x – 12.