**Radical Equations**

**Unit 6 Problems**

**Application problems including radical equations.**

Use radical equations to solve the following problems. Round all answers to the nearest tenth**. **

1. Vince wants to make a square patio in his yard. He has enough concrete to pave an area of 378 square feet. How long can a side of his patio be?

__Solution__

A square with sides a has an area given by;

Area = a^{2}

Hence;

a^{2} = 378

a = √378

a = 19.4 feet.

2. A hang glider dropped his cell phone from a height of 450 feet. How many seconds did it take for the cell phone to reach the ground?

__Solution__

Assuming that the drag of air is negligible, the cell phone was in free fall for the entire 450 feet to the ground.

Using the relationship below,

y = u.t+.a.t^{2}

hence,

450 = 0+..t^{2} =

= 450

t^{2} = √28.125s^{2}

t = 5.3 s

3. An accident investigator measured the skid marks of one of the vehicles involved in an accident. The length of the skid marks was 84 feet. What was the speed of the vehicle before the brakes were applied?

__Solution__

Let the speed of the car before skidding be s:

s = √24d

s = √(24x84)

s = √2016

s = 44.9 miles per hour.

4. How far from the base of the house do you need to place a 13-foot ladder so that it exactly reaches the top of a 10- foot tall wall?

__Solution__

Let the base of the 13-foot ladder be placed x ft away from the wall so that it exactly reaches 12-foot tall wall as shown below-:

Using Pythagoras theorem,

x^{2} = 13^{2}-10^{2}

x^{2} = 169-100

x = √69

x = 8.3-foot away from the wall.

5. A baseball diamond is a square that is 90 feet on each side. What is the distance a catcher has to throw the ball from home to second base?

__Solution:__

The baseball is a square and therefore, the throw from home plate to second base makes a hypotenuse side in a right angled triangle as shown below-:

Using Pythagoras theorem,

c^{2 }= 90^{2}+90^{2}

c = √ (90^{2}+90^{2})

c = 90√2

c = 127.3 Feet.

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