Squaring

square
Number Squared = Number × Itself = Number²


Basics
Number Squared = Number × Itself  = Number²

3 squared = 3 × 3 = 3² = 9
12 squared = 12 x 12 = 12² = 144
20 squared = 20 × 20 = 20² = 400

In order to get the correct answer when squaring a negative number, place the
negative number in parentheses to protect the order of operations.
Right:  -3 squared = (-3)² = 9
Wrong:  -3 squared = -3² = -9

square is the squaring command.

It is possible that questions involving squaring will be in the calculator-prohibited section of the test.  In that case, it is helpful to know your multiplication and division tables.


Formulas (NOT provided by Mathematics Formula Sheet)

Number Squared = Number × Itself = Number²


Question

What is 4²?

Answer
16

Calculator Click What You See Comment
clear blinker clears screen
square 4 squared
enter 16 Answer
Number²


Question
According to the calculator, what is the value of -4²?
According to the calculator, what is the value of (-4)²
?
Observe how parentheses change the results of these calculations.

Answer
-4² = -16
(-4)² = 16

Answer Process
The second calculation illustrates the way parentheses protect the order of operations when squaring a negative number.

Calculator Click What You See Comment
clear blinker clears screen
(-) 4 square -4²
enter -16
clear blinker clears screen
( (-) 4 ) square  (-4)²
Parentheses protect order of operations.
enter  16
Number²


Question

What is  \bf\displaystyle\frac{1}{4}  squared?

Answer
\bf\displaystyle\frac{1}{16}

Calculator Click What You See Comment
clear blinker clears screen
fraction 1 down 4 right square \bf\displaystyle{{\frac{1}{4}}^{2}} \bf\displaystyle\frac{1}{4}  squared
enter \bf\displaystyle\frac{1}{16} Answer
Number²


Question
What is 71.4 squared?

Answer
5097.96

Calculator Click What You See Comment
clear blinker clears screen
71.4 square 71.4² 71.4 squared
enter 5097.96 Answer
Number²


Question
Without using the calculator, what is 5 squared?

Answer
25

Answer Process
5 squared = 5² = 5 × 5 = 25


Question
Without using the calculator, what is -5 squared?

Answer
25

Answer Process
-5 squared = (-5)² = -5 × -5 = 25


Practice – Questions

1.  What is 9²?

2.  What is 9 squared?

3.  What is (-9)²?

4.  What is -9 squared?

5.  What is -9²?

6.  What is \bf\displaystyle\frac{1}{2} squared?

7.  What is \bf\displaystyle\frac{3}{4} squared?

8.  What is 313.25 squared?

9.  Without using the calculator, what is 7 squared?

10.  Without using the calculator, what is -7 squared?


Practice – Answers

1.  81

2.  81

3.  81

4.  81

5.  -81

6.  \bf\displaystyle\frac{1}{4}

7.  \bf\displaystyle\frac{9}{16}

8.  98125.5625

9.  49

10.  49

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