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प्रश्न
Observe the following pattern
22 − 12 = 2 + 1
32 − 22 = 3 + 2
42 − 32 = 4 + 3
52 − 42 = 5 + 4
and find the value of
992 − 962
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उत्तर
From the pattern, we can say that the difference between the squares of two consecutive numbers is the sum of the numbers itself.
In a formula:
`(n+1)^2-(n)^2=(n+1)+n`
संबंधित प्रश्न
From the pattern, we can say that the sum of the first n positive odd numbers is equal to the square of the n-th positive number. Putting that into formula:
1 + 3 + 5 + 7 + ... n = n2, where the left hand side consists of n terms.
Which of the following number is squares of even number ?
256
Find the squares of the following numbers using column method. Verify the result by finding the square using the usual multiplication:
54
Find the squares of the following numbers using diagonal method:
171
Find the square of the following number:
862
Find the square of the following number:
425
The sum of successive odd numbers 1, 3, 5, 7, 9, 11, 13 and 15 is ______.
The sum of two perfect squares is a perfect square.
Rahul walks 12 m north from his house and turns west to walk 35 m to reach his friend’s house. While returning, he walks diagonally from his friend’s house to reach back to his house. What distance did he walk while returning?
A 5.5 m long ladder is leaned against a wall. The ladder reaches the wall to a height of 4.4 m. Find the distance between the wall and the foot of the ladder.
