Grade 8 | Unit 8 | Lesson 1: The Areas of Squares and Their Side Lengths | Practice Problems

Find the area of each square. Each grid square represents 1 square unit.

• Square A, side length = square root of 17.

• Square B, side length = square root of 20.

• Square C, side length = square root of 13.

• Square D, side length = square root of 37.

Find the length of a side of a square if its area is: 81 square inches.

• 9 inches

• (\frac{4}{25}) cm

• 0.7 units

• (m) units

Find the length of a side of a square if its area is: (\frac{4}{25}) cm2.

• 9 inches

• (\frac{4}{25}) cm

• 0.7 units

• (m) units

Find the length of a side of a square if its area is: 0.49 square units.

• 9 inches

• (\frac{4}{25}) cm

• 0.7 units

• (m) units

Find the area of a square if its side length is: 3 inches.

• 9 square inches

• 49 square units

• 10,000 cm2

• 1,600 square inches

• (x^2) square units

Evaluate (3.1 \times 10^4) \boldcdot (2 \times 10^6). Choose the correct answer:

• A: (5.1 \times 10^{10})

• B: (5.1 \times 10^{24})

• C: (6.2 \times 10^{10})

• D: (6.2 \times 10^{24})

Do you agree with Noah’s solution to the problem? Evaluate each expression, giving the answer in scientific notation. The first problem part is: (5.4 \times 10^5 + 2.3 \times 10^4). Noah says, “I can rewrite (5.4 \times 10^5) as (54 \times 10^4). Now I can add the numbers: (54 \times 10^4 + 2.3 \times 10^4 = 56.3 \times 10^4).” Explain your reasoning.

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Select all the expressions that are equivalent to (3^8).

• A: (3^2)^4

• B: (8^3)

• C: (3 \boldcdot 3 \boldcdot 3 \boldcdot 3 \boldcdot 3 \boldcdot 3 \boldcdot 3 \boldcdot 3)

• D: (3^4)^2

• E: (\frac{3^6}{3^{\text-2}})