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Standard VIII

Mathematics

Random Interesting Patterns Followed by Square Numbers

Find the miss...

Question

Find the missing number of the pattern.
$3^{2} + 6^{2} + 18^{2} = 19^{2}$
$3^{2} + 4^{2} + 12^{2}$ = ___

13^{2}

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19^{2}

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7^{2}

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18^{2}

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Solution

The correct option is A $13^{2}$
From the pattern, the third number is the product of the first two number.
The fourth number can be obtained by adding 1 to the third number.
Then, the missing number will be
$4^{2} + 3^{2} + 12^{2} = 13^{2}$
So, $13^{2}$ is the missing number.

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Similar questions

Q. Using the given pattern, find the missing numbers:

1^{2} + 2^{2} + 2^{2} = 3^{2}

2^{2} + 3^{2} + 6^{2} = 7^{2}

3^{2} + 4^{2} + 12^{2} = 13^{2}

4^{2} + 5^{2} +

___

= 21^{2}

5^{2} +

___

+ 30^{2} = 31^{2}

6^{2} + 7^{2} +

___

=

____

Q. Using the given pattern, find the missing numbers.

1^{2} + 2^{2} + 2^{2} = 3^{2}

2^{2} + 3^{2} + 6^{2} = 7^{2}

3^{2} + 4^{2} + 12^{2} = 13^{2}

4^{2} + 5^{2} + . . . . . . = 21^{2}

5^{2} + . . . . . + 30^{2} = 31^{2}

6^{2} + 7^{2} + . . . . . . = . . . . . . . .

Question 6
Using the given pattern, find the missing numbers:
$1^{2} + 2^{2} + 2^{2} = 3^{2}$
$2^{2} + 3^{2} + 6^{2} = 7^{2}$
$3^{2} + 4^{2} + 12^{2} = 13^{2}$
$4^{2} + 5^{2} + {- --- -}^{2} = 21^{2}$
$5^{2} + {- --- -}^{2} + 30^{2} = 31^{2}$
$6^{2} + 7^{2} + - --- - 2 = - --- - 2$

Using the given pattern, find the missing numbers.

1² + 2² + 2² = 3²

2² + 3² + 6² = 7²

3² + 4² + 12² = 13²

4² + 5² + _ ² = 21²

5² + _ ² + 30² = 31²

6² + 7² + _ ² = __²

Q. Find the number of natural numbers lying between

18^{2}

19^{2}

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Find the missing number of the pattern.32+62+182=19232+42+122 = ___

The correct option is A 132From the pattern, the third number is the product of the first two number.The fourth number can be obtained by adding 1 to the third number.Then, the missing number will be42+32+122=132So, 132 is the missing number.

Find the missing number of the pattern.
$3^{2} + 6^{2} + 18^{2} = 19^{2}$
$3^{2} + 4^{2} + 12^{2}$ = ___

The correct option is A $13^{2}$
From the pattern, the third number is the product of the first two number.
The fourth number can be obtained by adding 1 to the third number.
Then, the missing number will be
$4^{2} + 3^{2} + 12^{2} = 13^{2}$
So, $13^{2}$ is the missing number.