9.6 Solve equations with square roots  (Page 4/6)

Police officers investigating car accidents measure the length of the skid marks on the pavement. Then they use square roots to determine the speed, in miles per hour, a car was going before applying the brakes.

After a car accident, the skid marks for one car measured 190 feet. Use the formula $s=\sqrt{24d}$ to find the speed of the car before the brakes were applied. Round your answer to the nearest tenth.

Solution

Step 1. Read the problem.
Step 2. Identify what we are looking for.	The speed of a car.
Step 3. Name what we are looking for.	Let s = the speed.
Step 4. Translate into an equation by writing the appropriate formula.
Substitute the given information.
Step 5. Solve the equation .
Round to 1 decimal place.
Step 6. Check the answer in the problem. $67.5\stackrel{?}{\approx }\sqrt{24\left(190\right)}$ $67.5\stackrel{?}{\approx }\sqrt{4560}$ $67.5\stackrel{?}{\approx }\mathrm{67.5277...}$
Is 67.5 mph a reasonable speed?	Yes.
Step 7. Answer the question with a complete sentence.	The speed of the car was approximately 67.5 miles per hour.

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Key concepts

• To Solve a Radical Equation:
  1. Isolate the radical on one side of the equation.
  2. Square both sides of the equation.
  3. Solve the new equation.
  4. Check the answer. Some solutions obtained may not work in the original equation.
• Solving Applications with Formulas
  1. Read the problem and make sure all the words and ideas are understood. When appropriate, draw a figure and label it with the given information.
  2. Identify what we are looking for.
  3. Name what we are looking for by choosing a variable to represent it.
  4. Translate into an equation by writing the appropriate formula or model for the situation. Substitute in the given information.
  5. Solve the equation using good algebra techniques.
  6. Check the answer in the problem and make sure it makes sense.
  7. Answer the question with a complete sentence.
• Area of a Square
  
• Falling Objects
  • On Earth, if an object is dropped from a height of $h$ feet, the time in seconds it will take to reach the ground is found by using the formula $t=\frac{\sqrt{h}}{4}$ .
• Skid Marks and Speed of a Car
  • If the length of the skid marks is d feet, then the speed, s , of the car before the brakes were applied can be found by using the formula $s=\sqrt{24d}$ .

Practice makes perfect

Solve Radical Equations