The square root of \[\dfrac{{{{\left( {0.75} \right)}^3}}}{{1 - \left( {0.75} \right)}} + \left( {0.75 + {{\left( {0.75} \right)}^2} + 1} \right)\] is
A) 1
B) 2
C) 3
D) 4

Hint: In order to get the square root of given expression first find cube and square of \[0.75\] so the that we can put it into the given equation and calculate one exact value for the given expression and then we will take the square root of that value which will make our calculation simpler and easier after that do the required addition, subtraction and division at the end take square root hence the answer will be obtained.

Complete step by step solution: Given: \[\dfrac{{{{\left( {0.75} \right)}^3}}}{{1 - \left( {0.75} \right)}} + \left( {0.75 + {{\left( {0.75} \right)}^2} + 1} \right)\]
To find: \[\sqrt {\dfrac{{{{\left( {0.75} \right)}^3}}}{{1 - \left( {0.75} \right)}} + \left( {0.75 + {{\left( {0.75} \right)}^2} + 1} \right)} \]
First we simplify the brackets,
\[ = \sqrt {\dfrac{{0.421875}}{{0.25}} + \left( {0.75 + 0.5625 + 1} \right)} \]
Now, on further simplification we get,
\[ = \sqrt {1.6875 + 2.3125} \]
Now on adding we get,
\[ = \sqrt 4 \]
Now on taking positive root we get,
\[ = 2 \]

Hence, option (B) 2 is the correct answer.

Note: Consider expressions that include one or more of the arithmetic operations: addition, subtraction, multiplication, and division. The order of operations requires that all multiplication and division be performed first, going from left to right in the expression. The order in which you compute multiplication and division is determined by which one comes first, reading from left to right.

After multiplication and division have been completed, add or subtract in order from left to right. The order of addition and subtraction is also determined by which one comes first when reading from left to right.

In order to simplify above question simplify using the BODMAS Rule i.e. brackets, orders of, division, multiplication, addition and subtraction. The rule says the order of calculation and also in order to get accurate answers do not round off the numbers.