1) Solve the following equations.
a) sqrt(x) - 1 = 4
b) sqrt(x^3) = 8
c) third root of x^2 = 4
2) Is sqrt(x^2) an identity (true for all values of x)?
Explain your answer in this space.
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 = s^3. Find the length of a side of a cube if the Volume is 729 cm3.
This solution looks at the calculations and algebra for the radical expressions in an attached Word document.