Definition of Perfect Square

Introduction to definition of perfect square:

The definition of perfect square is defined as the important topics in mathematics. Product of two integer gives another integer is known as the perfect square. The rational number with the square root is known as the perfect square.  For example, 16 is known as the perfect square integer, since it has 4  `xx`  4 is the two product for 16. This article shows the definition of perfect square with brief explanation and some example problems.


Explanation to definition of perfect square


The explanation given for the perfect square definition is as follows,

Trinomial and binomial functions are also written as the perfect square.
Trinomial Perfect square = x2 + 6x + 9
Trinomial Perfect square  = (x + 3)2 .
Perfect square Example:

0 , 1 , 4, 9, 16, 25, etc.

`16/36` , `16/25` are also the examples of perfect squares.


Example problems to definition of perfect square


Problem 1: Which of the following integer when added to 12 to make perfect square.

Options:

a) 2

b) 3

c) 1

d) 4

Solution:

Step 1: Given:

Number = 12

Step 2: To find:

Perfect square

Step 3: Solve:

12 + 4 = 16

16 = 42

16 = 4 `xx` 4

Therefore 4 is the integer when added to 12 to give perfect square.

Answer: Option d

Problem 2: Which of the following integer when added to 24 to make perfect square.

Options:

a) 2

b) 3

c) 1

d) 4

Solution:

Step 1: Given:

Number = 24

Step 2: To find:

Perfect square

Step 3: Solve:

24 + 1 = 25

25 = 52

16 = 5 `xx` 5

Therefore 1 is the integer when added to 24 to give perfect square.

Answer: Option c

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Practice problems to definition of perfect square


Problem 1: Which of the following integer when added to 25 to make perfect square.

Options:

a) 2

b) 1

c) 3

d) 4

Answer: Option b

Problem 2: Which of the following integer when added to 33 to make perfect square.

Options:

a) 2

b) 1

c) 3

d) 4

Answer: Option c

Perfect Squares

Introduction:

Square of number is multiply the same number twice.A × A =A2, here square of  A  is written as A2 Here A is called the base and 2 is called the index or the power.Now observe the following examples:

0^2 = 0 ×0 = 0

1^2 = 1 × 1 = 1

2^2 = 2 ×2 = 4

These examples are square the same number.The square of 0,1,2,3,4 are 0,1,4,9,16 respectively. These square numbers are known as perfect squares. I like to share this Transformations Geometry with you all through my article.


Explain perfect square with examples:


Examples:

1). Is 625 a perfect square?

Yes, because 625 can be expressed as the product of two same numbers as 25 × 25.

2). Is 10 a perfect square?

No, 10 is not a perfect square since 10 cannot be written as the product of two same numbers.

3). Is 144 a perfect square?

Yes, because 144 can be expressed as the product of two same numbers as 12 × 12.

4). Is 70 a perfect square?

No, 70 is not a perfect square since 70 cannot be written as the product of two same numbers. Understanding Graphing Calculators is always challenging for me but thanks to all math help websites to help me out.


Perfect square Examples:


(1). Find the Perfect square of 20

Solution:

20 ^2 = 20 * 20

= 400

(2). Find the Perfect square of 111

Solution:

111 2 = 111 * 111

= 12321

(3). Find the Perfect square of 13

Solution:

13^ 2 = 13 * 13

= 169

(4). Find the Perfect square of 81

Solution:

81^ 2 = 81*81

= 6561

(5). Find the Perfect square of 100

Solution:

100 ^2 = 100 * 100

= 10000

Perfect square Exercises:

(1). Find the Perfect square of 32

(2). Find the Perfect square of 15

(3). Find the Perfect square of 09

(4). Find the Perfect square of 723

(5). Find the Perfect square of 40

Answers:

(1). 1024

(2). 225

(3). 81

(4). 522729

(5). 1600