Question

Estimate the value of the square root: \[\dfrac{6}{{\sqrt 5 }}\] .

Answer 1

Hint: In this type of question first decode it then try to solve it, because here they are not telling you to find the value of \[{\sqrt 5 }\] they want you to find the value of \[\sqrt {\dfrac{6}{{\sqrt 5 }}} \] .

Complete step by step answer:
Let us try to find the value of \[{\sqrt 5 }\] first then we will try to find the value of \[\dfrac{6}{{\sqrt 5 }}\] and atlast when we will have all these square roots we fill be finding the value of \[\sqrt {\dfrac{6}{{\sqrt 5 }}} \] .
Now clearly we know that
\[\sqrt 5 = 2.23606\]
Now as we have this let us try to find the value of \[\dfrac{6}{{\sqrt 5 }}\]
i.e., \[\dfrac{6}{{\sqrt 5 }} = 2.683291\]
And when we have all these values clearly then \[\sqrt {\dfrac{6}{{\sqrt 5 }}} = \sqrt {2.683291} \]
Which will leave us with \[\sqrt {2.683291} = 1.638075\]

Note: In mathematics, a square root of a number x is a number y such that y2 = x; in other words, a number y whose square (the result of multiplying the number by itself, or y ⋅ y) is x. Again we must know that the square root of any negative number does not exist in real domain it exist in the complex domain which is also represented by i, where \[i = \sqrt { - 1} \] so if we have a number suppose \[\sqrt { - 9} \] then we know that it can be written as \[\sqrt {( - 1) \times 9} \] which is also \[\sqrt { - 1} \times \sqrt 9 = 3i\] .