Lesson 6

Select all solutions to the equation \(x^2=7\).

\(\sqrt{7}\)

\(\text- \sqrt7\)

49

-49

Find the solution(s) to each equation, if there are any.

1. \(x^2=9\)
2. \(\sqrt{x}=3\)
3. \(\sqrt{x}=\text-3\)

1. If \(c\) is a positive number, how many solutions does \(x^2=c\) have? Explain.
2. If \(c\) is a positive number, how many solutions does \(\sqrt{x}=c\) have? Explain.

Suppose that a friend missed class and never learned what \(37^{\frac13}\) means.

1. Use exponent rules your friend would already know to calculate \((37^{\frac13})^3\).
2. Explain why this means that \(37^{\frac13}\) is the cube root of 37.

Evaluate \(8^{\frac53}\).

Write each expression without using exponents.

1. \(5^{\frac23}\)
2. \(4^{\text-\frac32}\)