Radical Equations
Unit 7 Problems
Application problems including radical equations.
1. A positive real number is 4 less than another. When 8 times the larger is added to the square of the smaller, the result is 96. Find the numbers.
Solution
Let one number be x
The other number is x+4
8(x+4) + x2 = 96
8x+32x2 = 96
x2 + 8x - 64= 0
x2 + 8x +16 = 80
(x+4)2 = 80
x = -4-4√5
or x = -4+4√5
2. A positive real number is 4 less than another. If the sum of the squares of the two numbers is 72, then find the numbers.
Solution
Let one number be x
The other number is x+4
(x+4)2 + x2 = 72
x2+x2 + 8x + 16 = 72
x2 + 4x – 28 = 0
x2 + 4x = 28
(x+2)2 = 32
x = -2±√32
x= -2+√32
or x = -2+√32
3. The area of a rectangle is 46 square inches. If the length is 4 times the width, then find the dimensions of the rectangle. Round off your answers to the nearest hundredth.
Solution
x(4x) = 46
x2 - 46 = 0
4x2 = 46
x2 = 23
x2 = 11.5
x = -3.39
or
x = 3.39
ignore -3.39
Hence, the dimensions are;
Length = 3.39x4 =13.56 Inches
Width = 3.39 Inches.
4. If the sides of a square measure units, then find the length of the diagonal.
Solution
Let the length of the diagonal be x
X2 = (9√3)2 + (9√3)2
X2 = (81x3) + (81x3)
X2 = 486
X = 22.05 Units
5. The area of a rectangle is 20 square inches. If the length is 4 inches less than 6 times the width, then find the dimensions of the rectangle. Round off your answers to the nearest hundredth.
Solution
Let the width be x
Length = 6x-4
x(6x-4) = 20
x2-x-=0
(x-)=
Either x = -1.52(ignore)
Or x = 2.19
Length = 6(2.19)-4 = 9.14 Inches.
Width = 2.19 Inches.
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