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Question
Simplify the following using the identities: 1.73 × 1.73 − 0.27 × 0.27
Solution
Let us consider the following expression: \[1 . 73 \times 1 . 73 - 0 . 27 \times 0 . 27\]
Using the identity \[\left( a + b \right)\left( a - b \right) = a^2 - b^2\],we get:
\[1 . 73 \times 1 . 73 - 0 . 27 \times 0 . 27 = 1 . {73}^2 - 0 . {27}^2 = \left( 1 . 73 + 0 . 27 \right)\left( 1 . 73 - 0 . 27 \right) = 2 \times 1 . 46 = 2 . 92\]
Thus, the answer is 2.92.
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