Simplify each of the following:$ \frac{7.83 \times 7.83-1.17 \times 1.17}{6.66} $

Given:

\( \frac{7.83 \times 7.83-1.17 \times 1.17}{6.66} \)

To do:

We have to simplify the given expression.

Solution:

We know that,

$(a+b)^2=a^2+b^2+2ab$

$(a-b)^2=a^2+b^2-2ab$

$(a+b)(a-b)=a^2-b^2$

Therefore,

\( \frac{7.83 \times 7.83-1.17 \times 1.17}{6.66} \)

Let $a=7.83, b=1.17$

This implies,

$a-b=7.83-1.17=6.66$ and

$\frac{a \times a-b \times b}{a-b}=\frac{a^{2}-b^{2}}{a-b}$

$=\frac{(a+b)(a-b)}{a-b}$

$=a+b$

Therefore,

$\frac{7.83 \times 7.83-1.17 \times 1.17}{6.66}=7.83+1.17$

$=9.00$

$=9$

Hence, $\frac{7.83 \times 7.83-1.17 \times 1.17}{6.66}=9$.  

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Updated on: 10-Oct-2022

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