Question

How do you simplify \[\sqrt{\dfrac{3}{50}}\] ?

Answer 1

Hint: The square root problems like the one given above are very easy to understand and are simple to solve once we have a thorough idea of quadratic equations and polynomials. Having knowledge of these helps us to solve the problems much more smoothly and efficiently. For the given problem, we first apply the theory of rationalization in which we multiply the denominator and numerator by the denominator and after that we can easily take the denominator of the problem out of the given square root. In this problem, we multiply \[\sqrt{50}\] on both the numerator and the denominator, and evaluate the result accordingly.

Complete step by step answer:
Now we start off with the problem to the solution by writing that,
\[\sqrt{\dfrac{3\times 50}{50\times 50}}\]
Now, we can multiply the numerator terms and write the denominator in terms of a perfect square,
\[=\sqrt{\dfrac{150}{{{\left( 50 \right)}^{2}}}}\]
Now, from the above we can say that we take \[{{50}^{2}}\] common from the denominator, which due to the square root comes out to be \[50\] as common. Now, pulling it out, we can write it as,
\[=\dfrac{1}{50}\sqrt{150}\]
On factorising \[150\] with numbers which are perfect squares we can write it down as,
\[=\dfrac{1}{50}\sqrt{{{5}^{2}}\times 3\times 2}\]
Now, we take \[{{5}^{2}}\] out of the square root which turns out to be \[5\],
\[=\dfrac{5}{50}\sqrt{3\times 2}\]
Now, dividing both the numerator and the denominator by \[5\] we get,
\[=\dfrac{1}{10}\sqrt{6}\]
We can clearly observe now that the equation cannot be simplified further, hence this is our answer.

Note:
For problems like these we need to be thorough on our concepts and understanding regarding the theory of rationalization and square roots. We should also remember that while pulling a square of a number out of the square root, it results in the number itself, or else it would be in an irrational form. When we observe that the problem cannot be simplified further, we stop and we get the answer.