Introduction to Sum of two perfect squares:
In mathematics, a square number, sometimes also called a perfect square, is an integer that is the square of an integer; in other words, it is the product of some integer with itself. So, for example, 9 is a square number, since it can be written as 3 × 3. Square numbers are non-negative. Another way of saying that a (non-negative) number is a square number is that its square root is again an integer. For example, √9 = 3, so 9 is a square number.
(Source: Wikipedia)
Example for Sum of Two Perfect Squares:
Some of the examples for the sum of two perfect squares,
Example for sum of two perfect squares 1: `9, 100` find the sum of the perfect squares?
i) (9)
Solution:
`= 3^2`
`= 3 xx 3`
`= 9`
Therefore, 9 is a perfect square.
ii) 100 is a perfect square?
`= 10^2`
`= 10*10`
`= 100`
Therefore, `100 ` is a perfect square.
Therefore, sum of the perfect squares are,
`= 9 + 100`
`= 109`
Example for perfect square math 3: sqrt (64) is a perfect square?
`= 8 xx 8`
`= sqrt (64)`
Therefore, `sqrt (64)` is a perfect square.
Example for perfect square math 4: `(x + 6) ^2, (x + 5) ^2`
i) `(x +6)`
Solution: `= (x+6)2`
`= (x+6) (x+6)`
`= x(x+6) +6(x+6)`
`= x^2 + 6x + 6x + 64`
`= x^2 + 12x + 64`
There is another method also by using formula,
`= (x+6)^2 `
`= x^2 + 2 xx x xx 6 + 6^2 `
Therefore, `x^2+ 12x + 64 ` is a perfect square.
ii)` (x + 5)^2`
` = (x + 5) (x + 5)`
`= x(x + 5) + 5(x + 5)`
` = x^2 + 5x + 5x + 25`
` = x^2 + 10x + 25`
There is another method also by using formula,
`= (x + 5)^2`
`= x^2 + 2*x*5 + 5^2`
`= x^2 + 10x + 25`
Therefore, `x^2 + 10x + 25 ` is a perfect square.
Now, sum of those two perfect squares are taken,
`= (x^2+ 12x + 64)+ (x^2 + 10x + 25)`
` = 2x^2 + 22x + 99`
Please express your views of this topic cbse 10 sample papers by commenting on blog.
Practice Problem for Perfect Square Math:
Practice problem for perfect square math 1: `38, 50`
Answer: `3944`
Practice problem for perfect square math 2: `(x+9) ^2, (x + 8) ^2`
Answer: `2x^2 + 34x + 145`
In mathematics, a square number, sometimes also called a perfect square, is an integer that is the square of an integer; in other words, it is the product of some integer with itself. So, for example, 9 is a square number, since it can be written as 3 × 3. Square numbers are non-negative. Another way of saying that a (non-negative) number is a square number is that its square root is again an integer. For example, √9 = 3, so 9 is a square number.
(Source: Wikipedia)
Example for Sum of Two Perfect Squares:
Some of the examples for the sum of two perfect squares,
Example for sum of two perfect squares 1: `9, 100` find the sum of the perfect squares?
i) (9)
Solution:
`= 3^2`
`= 3 xx 3`
`= 9`
Therefore, 9 is a perfect square.
ii) 100 is a perfect square?
`= 10^2`
`= 10*10`
`= 100`
Therefore, `100 ` is a perfect square.
Therefore, sum of the perfect squares are,
`= 9 + 100`
`= 109`
Example for perfect square math 3: sqrt (64) is a perfect square?
`= 8 xx 8`
`= sqrt (64)`
Therefore, `sqrt (64)` is a perfect square.
Example for perfect square math 4: `(x + 6) ^2, (x + 5) ^2`
i) `(x +6)`
Solution: `= (x+6)2`
`= (x+6) (x+6)`
`= x(x+6) +6(x+6)`
`= x^2 + 6x + 6x + 64`
`= x^2 + 12x + 64`
There is another method also by using formula,
`= (x+6)^2 `
`= x^2 + 2 xx x xx 6 + 6^2 `
Therefore, `x^2+ 12x + 64 ` is a perfect square.
ii)` (x + 5)^2`
` = (x + 5) (x + 5)`
`= x(x + 5) + 5(x + 5)`
` = x^2 + 5x + 5x + 25`
` = x^2 + 10x + 25`
There is another method also by using formula,
`= (x + 5)^2`
`= x^2 + 2*x*5 + 5^2`
`= x^2 + 10x + 25`
Therefore, `x^2 + 10x + 25 ` is a perfect square.
Now, sum of those two perfect squares are taken,
`= (x^2+ 12x + 64)+ (x^2 + 10x + 25)`
` = 2x^2 + 22x + 99`
Please express your views of this topic cbse 10 sample papers by commenting on blog.
Practice Problem for Perfect Square Math:
Practice problem for perfect square math 1: `38, 50`
Answer: `3944`
Practice problem for perfect square math 2: `(x+9) ^2, (x + 8) ^2`
Answer: `2x^2 + 34x + 145`
