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Observe the following pattern 2^2-1^2=2...

Observe the following pattern `2^2-1^2=2+1` `3^2-2^2=3+2` `4^2-3^2=4+3` `5^2-4^2=5+4` and find the value of (I)`100^2-99^2` (ii) `111^2-109^2` (iii) `99^2-96^2`

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To solve the given problems, we will use the pattern observed in the provided equations. The pattern states that: \[ a^2 - b^2 = a + b \] where \( a \) and \( b \) are consecutive integers. ### Step-by-Step Solution: ...
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RD SHARMA-SQUARES AND SQUARE ROOTS-All Questions
  1. What will be the units digit of the squares of the following numbers...

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  2. Observe the following pattern 1+3=2^2 1+3+5=3^2 1+3+5+7=4^2 and...

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  3. Observe the following pattern 2^2-1^2=2+1 3^2-2^2=3+2 4^2-3^2=4+3 ...

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  4. Which of the following triplets are Pythagorean? (I)(8,\ 15 , 17) ...

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  5. Observe the following pattern (1xx2)+(2xx3)=(2xx3xx4)/3, (1xx2)+(2xx3...

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  6. Observe the following pattern 1=1/2{1xx(1+1)}, 1+2=1/2{2xx(2+1)}, 1...

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  7. Observe the following pattern (i)1^2=1/6[1xx(1+1)xx(2xx1+1)], (ii)1^...

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  8. Which of the following square numbers are squares of even numbers ? ...

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  9. By just examining the units digits, can you tell which of the follow...

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  10. Write five numbers for which you cannot decide whether they are squa...

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  11. Write five numbers which you connot decide whether they are square ...

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  12. Find the square root of the following number by prime factorization....

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  13. Find the squares of the following numbers using column method. (I)25...

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  14. Find the squares of the following numbers using column method: (I)99...

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  15. Find the squares of the following numbers by visual method. (I)54   ...

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  16. Find the square of the following numbers by visual method: (I)205   ...

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  17. Find the squares of the following using diagonal method: (I)89     ...

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  18. Find the square of the following numbers by diagonal method: (I)349 ...

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  19. Find the squares of the following numbers: (I)65            (ii)    ...

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  20. Find the squares of the following numbers: (I)56           (ii)  58 ...

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