Without squaring, find the values
i) $52^{2}$

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Solution

$52^{2} = {(50 + 2)}^{2} - (1)$
we have an algebric identity
${(a + b)}^{2} = a^{2} + b^{2} + 2 a b$
Using this we can write $(1)$ as
${(50 + 2)}^{2} = 50^{2} + 2^{2} + 2.50.2 = 2500 + 4 + 200 = 2500 + 200 + 4 = 2704$

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