Question
The square root of $$\frac{{{{\left( {0.75} \right)}^3}}}{{1 - 0.75}}$$ $${\text{ + }}$$$$\left[ {0.75 + {{\left( {0.75} \right)}^2} + 1} \right]$$ is = ?
Answer: Option B
$$\frac{{{{\left( {0.75} \right)}^3}}}{{1 - 0.75}}$$ $${\text{ + }}$$$$\left[ {0.75 + {{\left( {0.75} \right)}^2} + 1} \right]$$
$$ = \frac{{{{\left( {0.75} \right)}^2} \times 0.75}}{{0.25}}$$ $${\text{ + }}$$ $$\left[ {0.75 + 0.5625 + 1} \right]$$
$$ = 0.5625 \times 3 \,\, + $$ $$\left[ {0.75 + 0.5625 + 1} \right]$$
$$\eqalign{
& = 1.6875 + 2.3125 \cr
& = 4 \cr} $$
Square root of 4 = 2
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$$\frac{{{{\left( {0.75} \right)}^3}}}{{1 - 0.75}}$$ $${\text{ + }}$$$$\left[ {0.75 + {{\left( {0.75} \right)}^2} + 1} \right]$$
$$ = \frac{{{{\left( {0.75} \right)}^2} \times 0.75}}{{0.25}}$$ $${\text{ + }}$$ $$\left[ {0.75 + 0.5625 + 1} \right]$$
$$ = 0.5625 \times 3 \,\, + $$ $$\left[ {0.75 + 0.5625 + 1} \right]$$
$$\eqalign{
& = 1.6875 + 2.3125 \cr
& = 4 \cr} $$
Square root of 4 = 2
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