Question

Find the value of \[\sqrt {{3^{ - 2}}} \]

Answer 1

Hint: Here, we have to use the basic concept of the square root. Square root of a number is the factor that if we multiply itself by two times to get the original number. Firstly we have to write the given number in the simple form and then apply the square root formula. So by using the formula we will be able to find out the square root of the given number.

Formula used:
Square root of the number \[ = \sqrt {{\rm{number}}} \]

Complete step-by-step answer:
Given number is \[\sqrt {{3^{ - 2}}} \]
Firstly we will write the given number in the simple form by writing it as a fraction form for making its negative power to positive power for the simplification purpose.
Therefore, equation becomes \[\sqrt {\dfrac{1}{{{3^2}}}} \]
Now, from the above equation we can easily see that we have to find out the square root of the perfect square number\[\dfrac{1}{3}\]. Square root of a perfect square number is equal to the number itself.
Therefore, square root of given number i.e. \[\sqrt {\dfrac{1}{{{3^2}}}} = \dfrac{1}{3}\]
So, the value of the \[\sqrt {{3^{ - 2}}} \] is \[\dfrac{1}{3}\]
We can also write the value of \[\sqrt {{3^{ - 2}}} \] in the decimal form up to the three decimal places.
Hence, value of the \[\sqrt {{3^{ - 2}}} \]is \[0.334\]

Note: We don’t have to confuse square root with the cube root. The cube root of a number is the factor that if we multiply itself by three times to get the original number. Square root of any positive integer is possible but Square root of any negative number is not possible as square of any number is positive. Cube root of any integer is possible whether it is a positive number or negative number.
Square root is expressed as \[\sqrt {{\rm{number}}} \]
Cube root is expressed as \[\sqrt[3]{{{\rm{number}}}}\]