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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
1112 − 1092
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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`
1112 − 1092 = 1112 − 1102 + 1102 − 1092
= (111 + 110) + (110 + 109)
= 440
संबंधित प्रश्न
What will be the units digit of the square of the following number?
55555
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
Which of the following triplet pythagorean?
(10, 24, 26)
Observe the following pattern \[1 = \frac{1}{2}\left\{ 1 \times \left( 1 + 1 \right) \right\}\]
\[ 1 + 2 = \frac{1}{2}\left\{ 2 \times \left( 2 + 1 \right) \right\}\]
\[ 1 + 2 + 3 = \frac{1}{2}\left\{ 3 \times \left( 3 + 1 \right) \right\}\]
\[1 + 2 + 3 + 4 = \frac{1}{2}\left\{ 4 \times \left( 4 + 1 \right) \right\}\]
and find the values of following:
1 + 2 + 3 + 4 + 5 + ... + 50
Which of the following number are square of even number?
6561
Find the squares of the following numbers using column method. Verify the result by finding the square using the usual multiplication:
54
Find the square of the following number:
745
The sum of two perfect squares is a perfect square.
Write two Pythagorean triplets each having one of the numbers as 5.
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.
