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Find the square of the following numbers: $95$ .

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9025

9050

90100

9075

answer is A.

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Detailed Solution

Concept- First, we will write the given number in terms of the number for which we know the square. then proceed with the solution.
We must find 2 figures whose square is comprehended and by appertaining mathematical assignments we must get 95.

100, 5

95^{2}

95 = 100 - 5

(100 - 5)^{2}

a, b

100 = a

5 = b

(a - b)^{2}

(a - b) (a - b)

By distributive law:

a (b + c) = ab + ac

,we can write it:

a (a - b) - b (a - b)

By applying distributive law again, we get the terms as:

a^{2} - ab - ba + b^{2}

As a, b are numbers we know that

ab = ba

, is always true.

a^{2} - ab - ab + b^{2}

a^{2} - 2 ab + b^{2}

(a - b)^{2} = a^{2} - 2 ab + b^{2}

By substituting

a = 100, b = 5

(100 - 5)^{2} = (100)^{2} - 2 (100) (5) + (5)^{2}

95^{2} = 10000 - 1000 + 25

95^{2} = 10025 - 1000

95^{2} = 9025

Therefore, the required value is 9025.
Hence, the correct option is 1) 9025

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