Question

Evaluate:.....
$i) {0.9}^{2} - {0.5}^{2}$
$ii) {1.5}^{2} - {1.2}^{2}$
$iii)100. {5}^{2} - 99. {5}^{2}$

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Answer 1

The value (i) 0.56, (ii) 0.81 and (iii) 200

To solve this problem, we have to use a concept known as difference of two squares.

Difference of Two Squares

a)

Given two decimals and we are to find the difference between their squares,

$0.9^2 - 0.5^2\\(\frac{9}{10})^2 - (\frac{1}{2})^2 = \\ \frac{81}{100} - \frac{1}{4} = \frac{81 - 25}{100} = \frac{56}{100} = \frac{14}{25} = 0.56$

b)

We have two decimals

$1.5^2 - 1.2^2 = 2.25 - 1.44 = 0.81$

c)

We would find the difference of two squares here

$100.5^2 - 99.5^2 = 200$

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