# Algebra - Radical Equations

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1. At a height of h meters, you can see V kilometers to the horizon. These numbers are related by the equation . A person can see 392 km to the horizon from an airplane window. How high is the airplane?

2. The formula can be used to approximate the speed r, in miles per hour, of a car that has left skid marks of length L, in feet. How far will the car skid at 50 mph?

3. In the right triangle, find the length of the side not given. Give an exact answer and an approximation to three decimal places. What is the exact value for c?

4. Guy Wire. How long is a guy wire reaching from the top of a 15-ft pole to a point on the ground 10 feet from the pole.

5. Darla is building a new desk. To make sure she had made a square corner, she measures 4ft from the corner along the edge and 9ft from the corner along the other edge. How long should the diagonal be between those two points if the corner is a right angle?

10. Darla is building a new desk. To make sure she had made the corner, she measures 10ft from the corner along the edge and 6ft from the corner along the other edge. How long should the diagonal be between those two points if the corner is a right angle?

[Please the attached questions file.]

#### Solution Preview

The solution file is attached.

1. The solution for x =

Ö(5x) = 15 - 8 = 7

5x = 7^2 = 49

x = 49/5 = 9.8

2. The solution for y =

Squaring on both sides, we get 2y + 7 = 49

2y = 49 - 7 = 42

y = 21

3. The solution for x =

Cubing on both sides, we get x + 9 = 2^3 = 8

x = -1

4.

Squaring on both sides, we get 81 = 1/x x = 1/81

5. The solution is x =

3Ö(x - 1) = x - 1

Squaring on both sides, we get 9(x - 1) = (x - 1)^2

(x - 1)(x - 1 - 9) = 0

(x - 1)(x - 10) = 0

x = {1, 10}

6. The solution is z =

Squaring on both sides, we get 9 + z - 5 + 6Ö(z - 5) = z + 10

4 + z + 6Ö(z - 5) = z + 10

6Ö(z - 5) = 6 Ö(z - 5) = 1

Squaring on both sides, we get ...

#### Solution Summary

Radical equations in algebra are examined. Neat and step-by-step solutions are provided.