Question

How do you find the square root of $ 820 $ ?

Answer 1

Hint: The square root of a number is a number which on multiplying by itself gives the original number. We can find the square root of a number by different methods. For this question we will use the method of prime factorization to find the square root of $ 820 $ .

Complete step by step solution:
Given to us is a number $ 820 $ and we have to now find the square root of this number.
Let us use the method of prime factorization to find the square root of the given number.
The prime factorization of the number $ 820 $ is given as follows.
So now the number $ 820 $ can be written as the product of the factors of the number. This can be written as $ 820=2\times 2\times 5\times 41 $
Let us now apply square root on both sides of this equation. Now this becomes $ \sqrt{820}=\sqrt{2\times 2\times 5\times 41} $
We can also write this as $ \sqrt{820}=\sqrt{{{2}^{2}}\times 5\times 41} $
We can now further solve this to get $ \sqrt{820}=\sqrt{{{2}^{2}}}\times \sqrt{5\times 41} $
Since the number two is multiplied twice, it becomes a square. This square and its square root can be cancelled. We can now write this as $ \sqrt{820}=2\times \sqrt{5\times 41} $
Since the other numbers are not squares, they stay inside the root. We can now multiply this to get $ \sqrt{820}=2\sqrt{205} $
Therefore, the s square root of the given number is $ 2\sqrt{205} $ or $ \pm 2\sqrt{205} $
So, the correct answer is “ $ \pm 2\sqrt{205} $ ”.

Note: It is to be noted that a real number will have two square roots i.e. one negative and one positive. This is because the square of both these values give a positive real number. It should also be noted that the square root of a negative value is imaginary.