Square Brackets In Maths Formulas
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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