Question

How do you find the square root of $6561$?

Answer 1

In order to determine the square root of the number $6561$, first we have to find the factors of number $6561$ and choose the largest factor which is a perfect square. You will get that our number is a perfect square .Now writing the prime factors of $6561$you will get a answer of ${3^8}$and after putting this from the square root you will get an answer of ${3^4} = 81$.

Complete step by step solution:
We a given a number $6561$

Square root of any number is actually a number whose square gives back the original number.

So, square root of $6561$can be written as,
$= \sqrt {6561}$

Now , we’ll Separating the value $6561$ into its factors, So the factors of $6561$ comes to be,
$1,3,9,27,81,243,729,2187,6561$

Now let’s find the factors who are perfect squares of any number, we got
$1,9,81,729,6561$

So if see the largest number from above we found that it is the original number

If we find the prime factors of $6561$
We’ll get $6561 = 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3$

From the above we can say that $6561 = {3^8}$

Replace $6561$as ${3^8}$ in the original number
$= \sqrt {6561} \\\ = \sqrt {{3^8}} \\\ = {3^4} \\\ = 81 \\\$
Therefore, the square root of $\sqrt {6561}$in the simplest form is equal to $81$.

Additional Information:
A Perfect square is a number which can be easily expressed in terms of square of any number .

For example,$16$is a perfect square of number $4$as${4^2} = 16$.

Note: 1. Don’t Forgot to cross check the answer.
2.Factorise the number inside the square root properly to get knowledge of every perfect square.
3.Do the prime factorization carefully.