Find the positive solution to each equation. If the solution is irrational, write the solution using square root or cube root notation.

1. \(t^3=216\)
2. \(a^2=15\)
3. \(m^3=8\)
4. \(c^3=343\)
5. \(f^3=181\)

For each cube root, find the two whole numbers that it lies between.

1. \(\sqrt[3]{11}\)
2. \(\sqrt[3]{80}\)
3. \(\sqrt[3]{120}\)
4. \(\sqrt[3]{250}\)

Order the following values from least to greatest:

\(\displaystyle \sqrt[3]{530},\;\sqrt{48},\;\pi,\;\sqrt{121},\;\sqrt[3]{27},\;\frac{19}{2}\)

Select all the equations that have a solution of \(\frac{2}{7}\):

The equation \(x^2=25\) has two solutions. This is because both \(5 \boldcdot 5 = 25\), and also \(\text-5 \boldcdot \text-5 = 25\). So 5 is a solution, and \(\text-5\) is also a solution. But! The equation \(x^3=125\) only has one solution, which is 5. This is because \(5 \boldcdot 5 \boldcdot 5 = 125\), and there are no other numbers you can cube to make 125. (Think about why \(\text-5\) is not a solution!)

Find all the solutions to each equation.

1. \(x^3=8\)
2. \(\sqrt[3]x=3\)
3. \(x^2=49\)
4. \(x^3=\frac{64}{125}\)

Find the value of each variable, in units, to the nearest tenth.