Question

What is the square root of $[\frac{{\left(0.75\right)}^3}{1-0.75}+0.75+{\left(0.75\right)}^2+1]$?

• A. 1
• B. 2
• C. 3
• D. 4
• E. 5

Answer 1

The correct option is B

2

$\begin{array}{c}\sqrt{\frac{{\left(0.75\right)}^3}{\left(1-0.75\right)}+\left[0.75+{\left(0.75\right)}^2+1\right]}=\sqrt{\frac{{\left(0.75\right)}^3+\left(1-0.75\right)\left[{\left(1\right)}^2+{\left(0.75\right)}^2+1\times 0.75\right]}{1-0.75}}\\ =\sqrt{\frac{{\left(0.75\right)}^3+\left[{\left(1\right)}^3-{\left(0.75\right)}^3\right]}{1-0.75}}=\sqrt{\frac{1}{0.25}}=\sqrt{\frac{100}{25}}=\sqrt{4}=2\end{array}$