1) Solve the following equations.

a) \(\sqrt{x}-1=3\)

b) \(\sqrt{{{x}^{3}}}=8\).

c) \(\sqrt[3]{{{x}^{2}}}=4\)

2) Is \(\sqrt{{{x}^{2}}}=x\) an identity (true for all values of x)?

3) For the equation \(x-\sqrt{x}=0\), perform the following:

a) Solve for all values of x that satisfies the equation.

b) Graph the functions \(y=x\) and \(y=\sqrt{x}\) on the same graph (by plotting points if necessary). Show the points of intersection of these two graphs.

c) How does the graph relate to part a?

4) A right triangle is a triangle with one angle measuring 90°. In a right triangle, the sides are related by Pythagorean Theorem, \({{c}^{2}}={{a}^{2}}+{{b}^{2}}\) where c is the hypotenuse (the side opposite the 90° angle). Find the hypotenuse when the other 2 sides’ measurements are 3 feet and 4 feet.

5) Suppose you travel north for 35 kilometers then travel east 65 kilometers. How far are you from your starting point? North and east can be considered the directions of the y- and x-axis respectively.

6) The volume of a cube is given by V = s³. Find the length of a side of a cube if the

Volume is 729 cm³.

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