# 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}

**Solution:**

Let's find the missing squares in the pattern

The third number is the product of the first two numbers and the fourth number is obtained by adding 1 to the third number

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} + 20^{2} = 21^{2}

5^{2} + 6^{2} + 30^{2} = 31^{2}

6^{2} + 7^{2} + 42^{2} = 43^{2}

**☛ Check: **NCERT Solutions for Class 8 Maths Chapter 6

**Video Solution:**

## 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} . 4^{2} + 5^{2} + _^{2} = 21^{2} . 5^{2} + -^{2} + 30^{2} = 31^{2} . 6^{2} + 7^{2} + _^{2} = _^{2}

NCERT Solutions for Class 8 Maths Chapter 6 Exercise 6.1 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}

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

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

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

**Summary:**

For the given pattern, 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 }4^{2} + 5^{2} + _^{2} = 21^{2} 5^{2} + _^{2} + 30^{2} = 31^{2} 6^{2} + 7^{2} + _^{2} = _^{2}, the missing squares in the pattern are 20, 6 and 42 respectively.

**☛ Related Questions:**

- Without adding, find the sum. (i) 1 + 3 + 5 + 7 + 9 (ii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 +19 (iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23
- (i) Express 49 as the sum of 7 odd numbers. (ii) Express 121 as the sum of 11 odd numbers.
- How many numbers lie between squares of the following numbers? (i) 12 and 13 (ii) 25 and 26 (iii) 99 and 100
- Observe the following pattern and supply the missing numbers. 112 = 121 1012 = 10201 101012 = 102030201 10101012 = ? ?2 = 10203040504030201

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