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Byju's Answer

Standard VIII

Mathematics

Random Interesting Patterns Followed by Square Numbers

Find the miss...

Question

Find the missing number of the pattern.
$4^{2} + 2^{2} + 6^{2} = 36^{2}$
$5^{2} + 2^{2} +$ ___ = $49^{2}$

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 D $7^{2}$
From the pattern, the third number is the sum of the first two number.
The fourth number can be obtained by squaring the third number.
Then, the missing number will be
$5^{2} + 2^{2} + 7^{2} = 49^{2}$
So, $7^{2}$ 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} + . . . . . . = . . . . . . . .

Q. Find the missing number of the pattern.

3^{2} + 6^{2} + 18^{2} = 19^{2}

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

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

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Find the missing number of the pattern.42+22+62=36252+22+ ___ = 492

The correct option is D 72From the pattern, the third number is the sum of the first two number.The fourth number can be obtained by squaring the third number.Then, the missing number will be52+22+72=492So, 72 is the missing number.

Find the missing number of the pattern.
$4^{2} + 2^{2} + 6^{2} = 36^{2}$
$5^{2} + 2^{2} +$ ___ = $49^{2}$

The correct option is D $7^{2}$
From the pattern, the third number is the sum of the first two number.
The fourth number can be obtained by squaring the third number.
Then, the missing number will be
$5^{2} + 2^{2} + 7^{2} = 49^{2}$
So, $7^{2}$ is the missing number.