Question

What is the square root of 64?

Answer 1

Hint: To solve the given question, we should know some of the algebraic properties. We should know that \[\sqrt{a}\] can also be written as \[{{a}^{\dfrac{1}{2}}}\]. The other exponential property we should know is \[{{\left( {{a}^{m}} \right)}^{n}}={{a}^{mn}}\]. We will use these properties to find the value of the square root of 64.

Complete step-by-step solution:
We are asked to find a square root of 64. 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 64. By doing this, we get \[{{\left( 64 \right)}^{\dfrac{1}{2}}}\].
We know that 64 is a square of 8, thus we can write 64 as \[{{8}^{2}}\]. Putting this in the above expression we get \[{{\left( {{8}^{2}} \right)}^{\dfrac{1}{2}}}\].
Using the algebraic property \[{{\left( {{a}^{m}} \right)}^{n}}={{a}^{mn}}\], we can express above expression as \[{{8}^{2\times \dfrac{1}{2}}}\]. Cancelling out the common factors, we get 8.
Thus, the square root of 64 is 8.

Note: 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. We can also solve the given question directly by writing that as 64 is square of 8, its opposite is also true. That is, the square root of 64 is 8.