Question

Simplify the Square root of $ \sqrt {\dfrac{{27}}{6}} $

Answer 1

Hint: For simplifying this type of square root, we need to know the square root or cube root of a number. We must know both, it will be useful to us to solve according to the questions they ask. Here knowing the multiples of a number and cube of a number help you to solve this problem.

Complete step-by-step answer:
The given problem is,
 $ \sqrt {\dfrac{{27}}{6}} $
To solve this, we need to consider the cube root of $ 27 $ and factors of 6, to make you clear I am going to simplify term by term. Now I am considering the numerator term $ \sqrt {27} $ , and we can write it as $ \sqrt {3 \times 3 \times 3} $ . And now we need to consider the denominator term $ \sqrt 6 $ and it can be written as $ \sqrt {3 \times 2} $ , $ 3 $ and $ 2 $ are the factors of $ 6 $ . We need to simplify with respect to its numerator and denominator i.e..., I have written the factor of $ 6 $ as $ 3 \times 2 $ not as $ 6 \times 1 $ because I have $ 3 $ in the numerator so I can cancel the number $ 3 $ if I write the factors in the denominator in terms of the number $ 3 $ . Hence $ \sqrt {\dfrac{{27}}{6}} $ becomes,
$ = \sqrt {\dfrac{{3 \times 3 \times 3}}{{3 \times 2}}} $
Here, we can cancel the number $ 3 $ and the above term becomes,
= $ \sqrt {\dfrac{{3 \times 3}}{2}} $
Now, we have achieved our half task, now look at the terms, we have $ \sqrt {3 \times 3} $ in the numerator we can write it as $ 3 $ and hence the square root becomes,
$ = \dfrac{3}{{\sqrt 2 }} $
This is the answer for the square root $ \sqrt {\dfrac{{27}}{6}} $ . If we need to remove the root of the number $ 2 $ , then we need to convert it into decimal value.
So, the correct answer is “ $ \dfrac{3}{{\sqrt 2 }} $ ”.

Note: If you want to write it in decimal form, then you need to write the value of $ \sqrt 2 $ , which is $ 1.4142 $ and then divide $ \dfrac{3}{{1.4142}} $ , you will get an answer as $ 2.1213 $ . If you were asked this question in multiple choice questions, then you have an answer according to your option. If your option is given in the fraction, then you can stop with $ \dfrac{3}{{\sqrt 2 }} $ . If you need it in decimal form, then you need to solve more as I mentioned in the first line of the note