Question

How do you simplify $\sqrt {184} $ ?

Answer 1

Hint: In this question, we are given a number whose square root we have to find. We get the square of a number when a number is multiplied by itself. Thus, the square root is defined as the number whose square we found. Now, we have to find the square root of the number 184, that is, we have to find the number whose square is equal to 184. So for that, we write the number 184 as a product of its prime factors and then see if it can be written as a square of any number. Thus, after writing the given number as a square of another number, we can find out its square root.

Complete step by step solution:
On the factorization of 184, we get –
$
  184 = 2 \times 2 \times 2 \times 23 \\
   \Rightarrow 184 = {(2)^2} \times 46 \\
 $
Thus, $\sqrt {184} = 2\sqrt {46} $
Now, 46 cannot be written as a square of any integer, so we can find the square root of 46 by the calculator.

Hence, the square root of 184 is $ \pm 2\sqrt {46} $ or $ \pm 13.56466$ .

Note: In this question, we are given a simple number but in some problems, we may get asked to find the square root of a fraction or a negative number. For finding the square root of a fraction, we will first simplify it by canceling out the common factors and then find its square root. For finding the square root of a negative number we will write the number as a product of the positive number and -1, we have supposed $\sqrt { - 1} $ to be equal to iota denoted by $i$ . Thus $\sqrt { - {n^2}} = \pm ni$