Question

$\sqrt { \frac{(0.27)^2+(0.21)^2+(0.29)^2 }{(0.027)^2+(0.021)^2+(0.029)^2 }}$ =

• A. 10
• B. 100
• C. 0.1
• D. 0.01

Answer 1

Answer:

A. 10

Notice that:
$0.027 = \frac{0.27}{10}, \quad 0.021 = \frac{0.21}{10}, \quad 0.029 = \frac{0.29}{10}$

So each term in the denominator is $(\frac{1}{10})$ of the numerator term, and hence their squares are $(\frac{1}{100})$:

$(0.027)^2 = \frac{(0.27)^2}{100}, \quad (0.021)^2 = \frac{(0.21)^2}{100}, \quad (0.029)^2 = \frac{(0.29)^2}{100}$

Thus, the denominator becomes:
$\frac{(0.27)^2 + (0.21)^2 + (0.29)^2}{100}$

Now the expression is:
$\sqrt{\frac{(0.27)^2 + (0.21)^2 + (0.29)^2}{{\frac{(0.27)^2 + (0.21)^2 + (0.29)^2}{100}}}}$

$= \sqrt{100} = 10$

Final Answer:

10