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WORD PROBLEMS INVOLVING PERFECT SQUARES
Jump right to the exercises!
Here, you will solve word problems that result in equations involving perfect squares.
EXAMPLE:
I'm thinking of a number.
The square of 3 times this number is 25.
What number(s) could I be thinking of?
Solution:
(3x)2 = 25
3x = ±5
3x = 5 or 3x = -5
x = 5/3 or x = -5/3
EXAMPLE:
I'm thinking of a number.
When I take one less than three times this number, and then square the result,
I end up with the number 25.
What number(s) could I be thinking of?
Solution:
(3x-1)2 = 25
3x-1 = ±5
3x-1 = 5 or 3x-1 = -5
3x = 6 or 3x = -4
x = 2 or x = -4/3
EXAMPLE:
I'm thinking of a negative number.
When I take the sum of this number and 2, and then square the result,
I end up with the number 9.
What number am I thinking of?
Solution:
(x+2)2 = 9
x+2 = ±3
x+2 = 3 or x+2 = -3
x = 1 or x = -5
Since the number I'm thinking of is negative, the answer must be -5.
EXAMPLE:
I'm thinking of a positive number.
When I take the difference of this number and 3, and then square the result,
I end up with the number 16.
What number am I thinking of?
Solution:
(x-3)2 = 16
x-3 = ±4
x-3 = 4 or x-3 = -4
x = 7 or x = -1
Since the number I'm thinking of is positive, the answer must be 7.
On this exercise, you will not key in your answer.
However, you can check to see if your answer is correct.