Question

What is the square root of \[3\] divided by \[2\] \[?\]

Answer 1

Hint: To find the answer of the question firstly calculate the value of square root \[3\] using the long division method this will give some value in decimal which is infinite then use two techniques i.e. truncation and rounding to convert into finite figures and then divide the value by \[2\] .

Complete step by step answer:
Let us first get the detailed explanation of the term square root in mathematics. Square root of a number is some value which on multiplication by itself gives the original value. The symbol used to denote the square root is \[\sqrt{{}}\] . If we say \[y\] is the square root of \[x\] then mathematically it is represented as \[y=\sqrt{x}\] or we can say that \[{{y}^{2}}=x\] . If we square root any number then we have two values i.e. one positive value and one negative value. For example, if we have to find the square root of \[16\] then we get \[+4\] and \[-4\] as the result. But if we are willing to find the square root of negative numbers like \[-16\] then we have to learn about the complex numbers because the square root of the negative number is always negative. If any number is a perfect square then its perfect root will also exist.
In the question it is given that we have to find the value of square root of \[3\] divided by \[2\] \[?\] For that we have to firstly find the value of square root \[3\] . For finding the value of square roots the best method is the long division method. By using this method the value of the square root \[3\] is \[1.7320508075688\] this decimal value for the imperfect square root goes up to infinity. The value of an imperfect square root is a non-terminating decimal. But for the calculation purpose and to get the finite answer we use two techniques i.e. truncation and rounding. So after applying these two, we will get the value of square root \[3\] as \[1.732\] .
So if we divide \[1.732\] by \[2\] we will get \[0.866\] as the result.
Hence we can conclude that \[0.866\] is the answer to the given question.

Note: If any number whose unit digits are \[1,4,5,6\] or \[9\] then surely that whole number will have a perfect square root whereas, if the unit digits are \[2,3,7\] or \[8\] then the number will have imperfect square root. And if a number ends with an even number of zeros then also there is a perfect square root.