Question

What is the square root of \[2\] to the power \[2\] ?

Answer 1

Hint: These types of problems are pretty easy to solve once we clearly understand the key concepts behind the given question. In such problems, first of all we need to convert the theoretical statement of the problem into the mathematical form and then solve it according to our requirement. To evaluate this problem effectively, we need to have a clear cut idea of chapters like surds and square roots of numbers. In this particular problem, we need to find the square root of a given number. The general representation of the square root of any number ‘n’ is in the form of \[\sqrt{n}\] . Here according to the problem statement, the number given is described as \[2\] to the power of \[2\] , which is represented mathematically as \[{{2}^{2}}\]. We represent the square root of the number in the mathematical form as \[\sqrt{{{2}^{2}}}\] .

Complete step by step answer:
Now we start off with the solution to the given problem by trying to evaluate the value of \[\sqrt{{{2}^{2}}}=\sqrt{4}\] . We realise that the square of \[2\] is nothing but \[4\] . From this relation, we can easily find out that the square root of the number \[4\] or \[\sqrt{4}\] will be equal to \[2\] as the square of \[2\] is equal to \[\sqrt{4}\] . So our answer to the problem is equal to \[2\] .

Note: To solve these types of problems, we need to have some basic as well as advanced knowledge of surds and square root of numbers, or else we will not be able to solve the problem. We need to be careful while we write that a particular number is the square of another number. We also need to give additional attention when we are given decimal numbers, because it may sometimes be tricky to represent decimal numbers as the square of some other real number.