Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Solve each radical equation. Check your solution.

7. x + 3 = 5 square root of x plus 3 equals 5
8. t + 2 = 9 square root of t plus 2 equals 9
9. z − 1 = 5 square root of z minus 1 equals 5
10. n − 3 = 6 square root of n minus 3 equals 6
11. 2 b + 4 = 8 square root of 2 b end root , plus 4 equals 8
12. 3 − t = − 2 3 minus square root of t equals negative 2
13. 3 a + 1 = 7 square root of 3 eh plus 1 end root . equals 7
14. 10 b + 6 = 6 square root of 10 b plus 6 end root . equals 6
15. 1 = − 2 v − 3 1 equals . square root of negative 2 v minus 3 end root
16. x − 3 = 4 square root of x minus 3 end root , equals 4

See Problem 2.

17. Recreation You are making a tire swing for a playground. The time t in seconds for the tire to make one swing is given by t = 2 l 3.3 , t equals 2 , square root of l over 3.3 end root , comma  where ℓ is the length of the swing in feet. You want one swing to take 2.5 s. How many feet long should the swing be?
18. Geometry The length s of one edge of a cube is given by s = A 6 , s equals , square root of eh over 6 end root , comma  where A represents the cube's surface area. Suppose a cube has an edge length of 9 cm. What is its surface area? Round to the nearest hundredth.

See Problem 3.

Solve each radical equation. Check your solution.

19. 3 x + 1 = 5 x − 8 square root of 3 x plus 1 end root . equals . square root of 5 x minus 8 end root
20. 2 y = 9 − y square root of 2 y end root , equals , square root of 9 minus y end root
21. 7 v − 4 = 5 v + 10 square root of 7 v minus 4 end root . equals . square root of 5 v plus 10 end root
22. s + 10 = 6 − s square root of s plus 10 end root , equals , square root of 6 minus s end root
23. n + 5 = 5 n − 11 square root of n plus 5 end root , equals . square root of 5 n minus 11 end root
24. 3 m + 1 = 7 m − 9 square root of 3 m plus 1 end root . equals . square root of 7 m minus 9 end root

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