# simplify radical expression and solve quadratic equation

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1. Use property 2 to simply the following radical expression. sqrt(10/49)

2. Use the properties for radicals to simply the following expressions. Assume that all variables represent positive real numbers. sqrt(5/3), sqrt(12x^3/5)

3. simply by combining like terms: sqrt(63) - 2sqrt(28) + 5sqrt(7)

4. Geometry: Find the perimeter of the triangle shown in the figure

5. perform the indicated multiplication. Then simply each radical expression. sqrt(13) * sqrt(5).

6. sqrt(7)*(2sqrt(3) + 3sqrt(7)).

7. Perform the indicated division. Rationalize the denominator if necessary: (18 + sqrt(567) / 9

8. Geometry: find the area of rectangle shown in the figure.

9. solve each of the equations. Be sure to check your solutions.

10. Find the length x in each triangle, Express your answer in simplified radical form.

11. A homeowner wishes to insulate her attic with fiberglass and insulation to conserve energy. The insulation comes in 40cm wide rolls that are cut to fit between the rafters in the attic. If the roof is 7m from peak to eave and the attic space is 3m high at the peak, how long does each of the pieces of insulation need to be? Round to the nearest tenth.

12. Find the distance between the pair of points. (-3, 0) and (4, 0).

13. Geometry. The length of a rectangle is 1 cm longer than its width. If the diagonal of the rectangle is 5 cm, what are the dimensions of the rectangle? Use the Pythagorean theorem

14. Simply by combining the like terms: x*sqrt(18) - 3*sqrt(8*x^2)

15. Simplify the radical expression. (sqrt(3) + 5)(sqrt(3) - 3)

16. Find length x in the triangle. Express the answer in simplified radical form.

17. Solve the equation for x. 25x^2 = 3

18. Solve the equation for x. 2(x - 5)^2 = 3

19. Solve each of the following quadratic equations by completing the square.

21. Find two consecutive positive integers such that the sum of their squares is 85.

22. Use the quadratic formula to solve each of the following quadratic equations.

24. A garden area is 30 ft long and 20 ft wide. A path of uniform width is set around the edge. If the remaining garden area is 400 square ft, what is the width of the path?

25. Match the following graphs with the correct equation then describe the resulting graphs by identifying the vertex point, the graph's direction, and any axis intercepts gleaned from the table or graph.

26. Identify the axis of symmetry, create a suitable table of values and sketch the graph (including the axis of symmetry) and describe the resulting graphs by identifying the vertex point, the graph's direction, and any axis intercepts gleaned from the table or graph.

27. Find the x-intercept. y = x^2 +x - 6

28. A 80m ball is thrown upward from the roof of a building 100m tall with an initial velocity of 20 m/s. When will the ball reach a height of 80m (remember the constant is always equal to the initial height of the ball.

30. The demand and supply equations for certain type of printer is given by:

D = -200p + 35000, S = -p^2 + 400p - 20000

Find teh equilibrium price.

#### Solution Summary

The solution explains the basic operations such as simplifying, multiplication, and division, of radical expressions. It also shows how to solve quadratic equation using various techniques, such as factoring, completing squares, and quadratic formula.