Each of these expressions is a perfect square, which means that each can be written as something multiplied by itself.
Rewrite each expression as something multiplied by itself in the form . For example, can be rewritten as .
100
11.2
Activity
Perfect Squares in Different Forms
Each expression is written as the product of linear factors. Write an equivalent expression in standard form.
Why do you think the following expressions can be described as perfect squares?
11.3
Activity
Two Methods
Han and Jada solved the same equation with different methods. Here they are:
Han’s method:
Jada’s method:
Work with a partner to solve these equations. For each equation, one partner solves with Han’s method, and the other partner solves with Jada’s method. Make sure both partners get the same solutions to the same equation. If not, work together to find your mistakes.
Student Lesson Summary
These are some examples of perfect squares:
49, because 49 is or .
, because it is equivalent to or .
, because it is equivalent to .
, because it is equivalent to or .
A perfect squareis an expression that is something times itself. Usually we are interested in situations in which the something is a rational number or an expression with rational coefficients.
When expressions that are perfect squares are written in factored form and standard form, there is a predictable pattern.
is equivalent to .
is equivalent to .
is equivalent to .
In general, is equivalent to .
Quadratic equations that are in the form can be solved in a straightforward manner. Here is an example:
The equation now expresses that squaring gives 25 as a result. This means must be 5 or -5.
Glossary
perfect square
A perfect square is a number or an expression that is the result of multiplying a number or an expression to itself. In general, the multiplied number is rational and the multiplied expression has rational coefficients.
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