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Sum of squares formula Online - Tutorpace

# Sum of squares formula

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Sum of the squares formula is the formula to calculate the sum of the numbers which are squared. There are two types of formulas included in this case. One formula is when any two numbers are squared and the sum of squares can be calculated as, a2 + b2 = (a + b)2 – 2ab. The other formula is to find the sum of squares of first ‘n’ values and is given as: 12 + 22 + 32 + …+ n2 = n (n + 1) (2n + 1)/6.

Example 1: Calculate the sum of squares value of 22 + 52.

Solution: Given: sum of squares of 22 + 52
The formula for sum of squares in this case ==> a2 + b2 = (a + b)2 – 2ab
Here, a = 2 and b = 5
This gives: 22 + 52 = (2 + 5)2 – 2* 2* 5
This implies: 22 + 52 = 72 – 20 ==> 49 – 20 = 29.
Therefore, the sum of squares of 22 + 52 is 29.

Example 2: Calculate the sum of squares value of first 6 numbers.

Solution: Sum of squares of first 6 numbers==> 12+ 22+ 32+ 42+ 52+ 62
Sum of squares of first ‘n’ numbers is:
12+ 22+ 32+ …+n2 = [n (n+ 1) (2n+ 1)]/6
Given n= 6
This gives: 12 + 22 + 32 + 42 + 52 + 62 = [6 (6+ 1) (2* 6 + 1)]/ 6
This gives: Sum of squares= (6 * 7 * 13)/ 6= 91
Therefore, the sum of squares of first 6 numbers is 91.