Lesson 2
Square Roots and Cube Roots
- Let’s think about square and cube roots.
Problem 1
Rewrite the following expression as a number with no exponents. Explain or show your reasoning.
\(\displaystyle \dfrac{7^{\text-3}}{7^{\text-5}}\)
Problem 2
Find the value of each variable that makes the equation true.
- \((2^d)^4 = 2^{12}\)
- \(3^5 \boldcdot 7^5 = e^5\)
- \(5^0 \boldcdot 5^f = 5^4\)
Problem 3
A square has area 9 cm2. How long are its sides?
A:
3 cm
B:
4.5 cm
C:
9 cm
D:
81 cm
Problem 4
The table shows the side length and area of several different squares. Complete the table using exact values.
side length (cm) | 5 | \(\sqrt{63}\) | \(\sqrt{125}\) | |||
---|---|---|---|---|---|---|
area (cm2) | 49 | 98 | 102 |
Problem 5
Find the two whole numbers that are the closest to \(\sqrt{42}\). Explain your reasoning.