 # Solve Square Root Word Problems

Video lessons with examples and solutions that will help students solve square root word problems.

How to solve word problems with square root functions?
Examples:
1. Boat builders share an old rule of thumb for sailboats. The maximum speed K in knots is 1.35 times the square root of the length L in feet of the boat's waterline. A customer is planning to order a sailboat with a maximum speed of 8 knots. How long should the waterline be?
2. The circular velocity, v, in miles per hour, of a satellite orbiting Earth is given by the formula $$v = \sqrt {\frac{{1.24 \times {{10}^{12}}}}{r}}$$, where r is the distance in miles from the satellite to the center of the Earth. How much greater is the velocity of a satellite orbiting at an altitude of 100 mi than one orbiting at 300 mi? (The radius of the earth is 3950 mi)
Square Root Application
This video shows how to use the square root function in word problems.
Example:
The speed s in miles per hour that a car is traveling when it goes into a skid can be estimated by using the formula $$s = \sqrt {30fd}$$, where f is the coefficient of friction and d is the length of the skid marks in feet.
A car skids to a stop on a street with a speed limit of 30 mi/h. THe skid marks measure 35 ft, and the coefficient of friction was 0.7. Was the car speeding? Explain.

Application Involving a Square Root
A word problem that involves a formula that contains a square root.
Example:
The speed of a vehicle before the brakes were applied can be estimated by the length of the skid marks left on the road. On wet concrete, the speed v in miles per hour can be estimated by the formula $$v = 2\sqrt {3d}$$, where d represents the length of the skidmarks in feet. Estimate the speed of the vehicle f the skidmarks measure 27 feet.
GMAT Test on Square roots
Example:
If y is the smallest positive integer such that 3,150 multiplied by y is the square of n integer, then y must be?

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