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# Radicals and Rational Exponents and Pythagorean Theorem

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1) Solve the following equations.
a)
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b)
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c)
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2) Is an identity (true for all values of x)?

3) For the equation , perform the following:
a) Solve for all values of x that satisfies the equation.
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b) Graph the functions y = x and on the same graph (by plotting points if necessary). Show the points of intersection of these two graphs.
Graph:

Points of intersection:

4) A right triangle is a triangle with one angle measuring 90°. In a right triangle, the sides are related by Pythagorean Theorem, , where c is the hypotenuse (the side opposite the 90° angle). Find the hypotenuse when the other 2 sides' measurements are 6 feet and 8 feet.
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5) Suppose you travel north for 65 kilometers then travel east 75 kilometers. How far are you from your starting point?
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6) The volume of a cube is given by V = s3. Find the length of a side of a cube if the Volume is 1000 cm3.