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subject: Square Brackets In Maths Formulas [print this page]

The square brackets are used generally in mathematics formulas and problems. It can also be used to represent an interval. The notation can be used as [x, z) to denote the interval from x to z that is exclusive of z. Thus the number can be given as, [6, 12) would be the set of all real numbers between 6 and 12 where the numbers includes from 5 to 11 only.

About the Square Brackets in Maths Formulas:

The square brackets are used to group the numbers such as the variables, terms and constants and it includes the parenthesis brackets also.

Ex : 6[1+2+(y+2)2 +3(a2+b2)] = 0.

This can be written as,

6[1 + 2 + y2 + 2y + 4 + 4a2 + 4b2] = 0

The next item 5 to be multiply with all the terms

6 + 12 + 6y2 + 12y + 24 + 24a 2 + 24b2 = 0.

Some example formulas in maths using square brackets:

The formula for (a3 + b3) given as follows,

1. (a3 + b3) = [(a + b)(a2 ab + b2)]

= [(a + b)3 3ab(a + b)]

= (a+b)[(a+b)2-3ab]

= (a+b)(a2-ab+b2)

2. (a+b+c)3 = [(a + b + c)(a + b + c)(a + b + c)]

First we have to multiply the parenthesis brackets are inside and we get.

a3 + 3a2b + 3a2c + 3ab2 + 6abc + 3ac2 + b3 + 3b2c + 3bc2 + c3

Problems in Maths Using the Square Brackets:

Ex 1: Determine the value of (1004)3.

Sol : First take the given value and write the cube formula,

(a+b)3=a3+b3+3ab(a+b)

Substitute the value in the above formula

(1004)3 = (1000+4)3

Expand the values according to the formula

(1000+4)3 = [(1000)3] + 3[(1000)2x4] + 3[1000(4)2+ (4)3]

Now multiply the numbers which are in the parenthesis brackets

(1000+4)3 = [1000000000+12000000+48000+64]

(1004)3 = 1,012,048,064.

Ex 2 : Determine the value of (198)3.

Sol : The value can be simplified using the formula,

(a - b)3 = a3 - 3a2b + 3ab2 - b3

= a3 - b3 - 3ab (a - b)

(198)3 = (200-2)3

Now expand the vlaues with the help of the formula

(198)3 = (200)3-3(200)2x2+3x200(2)2-(2)3

Multiply the values we get,

(198)3 = 8000000-240000+2400-8

(198)3 = 7,762,392.

Check this how many prime numbers from 1 to 100 awesome i recently used to see.

Sum of square numbers are one of the basis for mathematics. Sum of square numbers are represented by x2 +y2 . The sum of square numbers are also represented as the perfect square. For example, if 64 is a square number, then it can be also be represented as 8'xx' 8. All number are said to be square numbers. The number 1 is not a square number.

Explanation for Sum of Square Numbers

Some of examples for the square numbers are represented as, 22 , 33 ,42 , 52 etc, are said to be square numbers.

Some of the condition for square numbers are,

1. If suppose the number is ends with 0 means, then the square numbers are also ends with 00.

2. If suppose the number is ends with 1 or by 9 means, then the square numbers are ends with 1.

3.If suppose the number is ends with 2 or by 8 means, then the square numbers are ends with 4.

4.If suppose the number is ends with 3 or by 7 means, then the square numbers are also ends with 9.

5.If suppose the number is ends with 4 or by 6 means, then the square numbers are also ends with 6.

6.If suppose the number is ends with 5 means, then the square numbers are also ends with 25.

Example Problem for Sum of Square Numbers

Problem 1: Find the sum of given square numbers. 82 + 62 .

Solution:

Step 1: In the first step, find the square numbers for the given function.

82 = 64

62 = 36

Step 2: Add the obtained square numbers. Therefore we get,

= 82 + 62

= 64 + 36

=100.

This is the required solution for the sum of square numbers.

Problem 1: Find the sum of given square numbers. 42 + 52 .

Solution:

Step 1: In the first step, find the square numbers for the given function.

42 = 16

52 = 25

Step 2: Add the obtained square numbers. Therefore we get,

= 42 + 52

= 16 + 25

=36

This is the required solution for the sum of square numbers.

by: mathqa

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