Question 136464
1. find the exact length of the side of a square which has a diagonal of 100 feet.
Draw the picture of a square and its diagonal of 100 ft.
Label each of the sides as "x".
Use Pythagoras to get:
100^2 = x^2 + x^2
2x^2 = 100^2
x^2 = 2*100^2
x = 100*sqrt(2) ft.
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2. The hypotenuse of a right triangle measures 100 inches, and one leg measures 50 inches. Find the measure of the other leg.
100^2 = 50^2 + x^2
x^2 = 100^2 - 50^2
x^2 = 7500
x^2 = 2500*3
x = 50*sqrt(3) inches
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a. give its length in simplified radical form.: 50*sqrt(3) inches
b. Round the answer to the nearest thousandth.86.6025... 
3. 10 the square root of 250x - 10 the square root of 160x + 6 the square root of 10x
10*sqrt(250)x - 10*sqrt(160)x + 6*sqrt(10)x
=  50*sqrt(10)x - 4*sqrt(10)x + 6*sqrt(10)x
=  52*sqrt(10)x
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4.(the square root of x - 9) ( the square root of x + 9)
Use FOIL:
F: sqrt(x)*sqrt(x) = x
O: 9*sqrt(x)
I:-9*sqrt(x)
L: -9*9= -81
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Ans: x-81
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Cheers,
Stan H.