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Sum of Squares Formula

The formula used to calculate the sum of two or more squares is the Sum of squares formula. To describe how well a model represents the data being modelled, the sum of squares formula is used. The sum of square is the measure of deviation from the data’s mean value. Hence, it is calculated as the total summation of the squares minus from the mean.

The formula to calculate the sum of the squares of two values is given as,

\[\large a^{2}+b^{2}=\left(a+b\right)^{2}-2ab\]

The Sum of Squares Formula for N values is given as,

\[\large 1^{2}+2^{2}+3^{2}…….n^{2}=\frac{n\left(n-1\right)\left(2n-1\right)}{6}\]

Solved example

Question: What is the value of $4^{2}+10^{2}$ ?

Solution:

The formula for sum of squares is: $a^{2}+b^{2}=\left(a+b\right)^{2}-2ab$ 

From the given equation: a=4 and b=10

$4^{2}+10^{2}=\left(4+10\right)^{2}-2(4)(10)$

$=196-2\left(14\right)$

$=196-28$

$=168$

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