Question

What is the square root of 4?

Answer 1

Hint: To solve the given question, we should know some of the algebraic properties. We should know that \[{{\left( {{a}^{m}} \right)}^{n}}={{a}^{mn}}\]. The other exponential property we should know is \[\sqrt{a}\] can also be written as \[{{a}^{\dfrac{1}{2}}}\]. We will use these properties to find the value of the square root of 4.

Complete step by step solution:
We are asked to find a square root of 4. We need to simplify and find its value. The given expression is of the form \[\sqrt{a}\], we know it can also be written as \[{{a}^{\dfrac{1}{2}}}\], here we have the value of a as 4. By doing this, we get \[{{\left( 4 \right)}^{\dfrac{1}{2}}}\].
We know that 4 is square of 2, thus we can write 4 as \[{{2}^{2}}\]. Putting this in the above expression we get \[{{\left( {{2}^{2}} \right)}^{\dfrac{1}{2}}}\].
Using the algebraic property \[{{\left( {{a}^{m}} \right)}^{n}}={{a}^{mn}}\], we can express above expression as \[{{4}^{2\times \dfrac{1}{2}}}\]. Cancelling out the common factors, we get 2.

Thus, the square root of 4 is 2.

Note: We can also solve the given question directly by writing that as 4 is square of 2, so the opposite of this statement is also true. That is, the square root of 4 is 2. To solve these types of questions, we should know the squares and square roots of different numbers. While calculating the square root a number which is not a perfect square. If we are asked to round the result to a certain digit then do it. If not then leave the expression in the radical form.