Lesson 6
Squares and Square Roots
- Let’s compare equations with squares and square roots.
Problem 1
Select all solutions to the equation \(x^2=7\).
A:
\(\sqrt{7}\)
B:
\(\text- \sqrt7\)
C:
49
D:
-49
Problem 2
Find the solution(s) to each equation, if there are any.
- \(x^2=9\)
- \(\sqrt{x}=3\)
- \(\sqrt{x}=\text-3\)
Problem 3
- If \(c\) is a positive number, how many solutions does \(x^2=c\) have? Explain.
- If \(c\) is a positive number, how many solutions does \(\sqrt{x}=c\) have? Explain.
Problem 4
Suppose that a friend missed class and never learned what \(37^{\frac13}\) means.
- Use exponent rules your friend would already know to calculate \((37^{\frac13})^3\).
- Explain why this means that \(37^{\frac13}\) is the cube root of 37.
Problem 5
Evaluate \(8^{\frac53}\).
Problem 6
Write each expression without using exponents.
- \(5^{\frac23}\)
- \(4^{\text-\frac32}\)