Lesson 1

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

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

1. 81 square inches
2. \(\frac{4}{25}\) cm²
3. 0.49 square units

4. \(m^2\) square units

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

1. 3 inches
2. 7 units
3. 100 cm
4. 40 inches
5. \(x\) units

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

\(5.1 \times 10^{10}\)

\(5.1 \times 10^{24}\)

\(6.2 \times 10^{10}\)

\(6.2 \times 10^{24}\)

Noah reads 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: \(54 \times 10^4 + 2.3 \times 10^4 = 56.3 \times 10^4\).”

Do you agree with Noah’s solution to the problem? Explain your reasoning.

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

\((3^2)^4\)

\(8^3\)

\(3 \boldcdot 3 \boldcdot 3 \boldcdot 3 \boldcdot 3 \boldcdot 3 \boldcdot 3 \boldcdot 3\)

\((3^4)^2\)

\(\frac{3^6}{3^{\text-2}}\)

\(3^6 \boldcdot 10^2\)