Question
$$\sqrt {110.25} \times \sqrt {0.01} \, \div $$ $$\sqrt {0.0025} $$ $$ - $$ $$\sqrt {420.25} $$ equals ?
Answer: Option A
Given expression,
$$ = \sqrt {\frac{{11025}}{{100}}} \times \sqrt {\frac{1}{{100}}} \, \div \,$$ $$\sqrt {\frac{{25}}{{10000}}} \, - \,$$ $$\,\sqrt {\frac{{42025}}{{100}}} $$
$$\eqalign{
& = \frac{{105}}{{10}} \times \frac{1}{{10}} \div \frac{5}{{100}} - \frac{{205}}{{10}} \cr
& = \frac{{105}}{{100}} \times \frac{{100}}{5} - \frac{{205}}{{10}} \cr
& = 21 - \frac{{205}}{{10}} \cr
& = \frac{{210 - 205}}{{10}} \cr
& = \frac{5}{{10}} \cr
& = \frac{1}{2} \cr
& = 0.50 \cr} $$
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Given expression,
$$ = \sqrt {\frac{{11025}}{{100}}} \times \sqrt {\frac{1}{{100}}} \, \div \,$$ $$\sqrt {\frac{{25}}{{10000}}} \, - \,$$ $$\,\sqrt {\frac{{42025}}{{100}}} $$
$$\eqalign{
& = \frac{{105}}{{10}} \times \frac{1}{{10}} \div \frac{5}{{100}} - \frac{{205}}{{10}} \cr
& = \frac{{105}}{{100}} \times \frac{{100}}{5} - \frac{{205}}{{10}} \cr
& = 21 - \frac{{205}}{{10}} \cr
& = \frac{{210 - 205}}{{10}} \cr
& = \frac{5}{{10}} \cr
& = \frac{1}{2} \cr
& = 0.50 \cr} $$
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