Question

Find the square root $\sqrt {\dfrac{{9.5 \times 0.58}}{{0.0017 \times 0.19}}}$

Answer 1

Hint: Firstly, convert the decimals back into fractions. Write them in such a way that powers $10\;$ are in its denominator. Now try to convert all the fractions into one single fraction and simplify. Simplify the constant in the denominator to the constants in the numerator only if they are multiples of each other. Evaluate and then finally find the square of the singular constant or decimal.

Complete step-by-step solution:
The given expression is, $\sqrt {\dfrac{{9.5 \times 0.58}}{{0.0017 \times 0.19}}}$
Now convert the decimals into fractions. That is, write the denominators in terms of $10\;$ .
$\Rightarrow \sqrt {\dfrac{{\dfrac{{95}}{{10}} \times \dfrac{{58}}{{100}}}}{{\dfrac{{17}}{{10000}} \times \dfrac{{19}}{{100}}}}}$
Now convert all these fractions into a single fraction.
$\Rightarrow \sqrt {\dfrac{{95 \times 58}}{{1000}} \times \dfrac{{1000000}}{{17 \times 19}}}$
Now cancel the terms which are multiples in the numerator and the denominator.
$\Rightarrow \sqrt {\dfrac{{95 \times 58}}{1} \times \dfrac{{1000}}{{17 \times 19}}}$
Always write the multiplied product in expanded form to easily cancel out the terms in the numerator and the denominator.
Now simplify further by writing $95\;$ in terms of $19\;$ or the multiples of it so that we can cancel easily.
$\Rightarrow \sqrt {\dfrac{{\left( {\dfrac{{190}}{2}} \right) \times 58}}{1} \times \dfrac{{1000}}{{17 \times 19}}}$
Simplify further to get,
$\Rightarrow \sqrt {\dfrac{{190 \times 58}}{2} \times \dfrac{{1000}}{{17 \times 19}}}$
$\Rightarrow \sqrt {\dfrac{{10 \times 58}}{2} \times \dfrac{{1000}}{{17 \times 1}}}$
Now as we can see that there is still some more simplification.
$\Rightarrow \sqrt {\dfrac{{10 \times 29}}{1} \times \dfrac{{1000}}{{17 \times 1}}}$
Now since we can’t further simplify just multiply all the terms in the numerator and the denominator and write a single fraction.
$\Rightarrow \sqrt {\dfrac{{29 \times 10000}}{{17}}}$
$\Rightarrow \sqrt {\dfrac{{290000}}{{17}}}$
Now perform division to the fraction inside the square root.
$\Rightarrow \sqrt {17058.8235}$
Now upon finding the square root we get,
$\Rightarrow 130.609$

$\therefore$ The solution to the expression $\sqrt {\dfrac{{9.5 \times 0.58}}{{0.0017 \times 0.19}}}$ is $130.609\;$

Note: Always check the number of decimal places (number of digits) after the decimal place to convert the decimal into a fraction. The number of digits is then written to the power of $10\;$ and then placed in the denominator and in the numerator, the number will be written the same as it is, but without the decimal point.