﻿ Word Problems Involving Perfect Squares
WORD PROBLEMS INVOLVING PERFECT SQUARES
by Dr. Carol JVF Burns (website creator)
Follow along with the highlighted text while you listen!

Here, you will solve word problems that result in equations involving perfect squares.

EXAMPLES:
Question: I'm thinking of a number.
The square of $\,3\,$ times this number is $\,25\,$.
What number(s) could I be thinking of?
Solution:

$(3x)^2 = 25$

$3x = \pm 5$

$3x = 5\ \ \text{or}\ \ 3x = -5$

$x = \frac{5}{3}\ \ \text{or}\ \ x = -\frac{5}{3}$
Question: 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:

$(3x-1)^2 = 25$

$3x-1 = \pm 5$

$3x-1 = 5\ \ \text{or}\ \ 3x-1 = -5$

$3x = 6\ \ \text{or}\ \ 3x = -4$

$x = 2\ \ \text{or}\ \ x = -\frac{4}{3}$
Question: 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:

$(x+2)^2 = 9$

$x+2 = \pm 3$

$x+2 = 3\ \ \text{or}\ \ x+2 = -3$

$x = 1\ \ \text{or}\ \ x = -5$

Since the number being thought of is negative, the answer is $\,-5\,$.
Question: 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:

$(x-3)^2 = 16$

$x-3 = \pm 4$

$x-3 = 4\ \ \text{or}\ \ x-3 = -4$

$x = 7\ \ \text{or}\ \ x = -1$

Since the number being thought of is positive, the answer is $\,7\,$.
Master the ideas from this section

When you're done practicing, move on to:
Basic Concepts Involved in Factoring Trinomials

CONCEPT QUESTIONS EXERCISE: