Question

How do you find the square root of 405?

Answer 1

Hint: Square root of a number is a value, which on multiplied by itself gives the original number. Suppose, ‘x’ is the square root of ‘y’, then it is represented as \[x = \sqrt y \] or we can express the same equation as \[{x^2} = y\] . Here we can see that 405 is not a perfect square. To solve this we factorize the given number.

Complete step-by-step answer:
Given, square root of 405.
That is, \[\sqrt {405} \]
405 can be factorized as,
 \[405 = 1 \times 3 \times 3 \times 3 \times 3 \times 5\]
We can see that 3 is multiplied four times, we multiply that we get,
 \[405 = 81 \times 5\] .
Then,
 \[ \Rightarrow \sqrt {405} = \sqrt {81 \times 5} \]
Since we know that 81 is a perfect square we can take this outside of the square root we have,
 \[ = 9\sqrt 5 \] . This is the exact form. We can stop here.
We also put it in the decimal form.
We know that \[\sqrt 5 = 2.236\] and multiplying this with 9 we get,
 \[ = 9 \times 2.236\]
 \[ = 20.124\] . This is the decimal form.
So, the correct answer is “20.124”.

Note: Here \[\sqrt {} \] is the radical symbol used to represent the root of numbers. The number under the radical symbol is called radicand. The positive number, when multiplied by itself, represents the square of the number. The square root of the square of a positive number gives the original number. To find the factors find the smallest prime number that divides the given number and divide it by that number, and then again find the smallest prime number that divides the number obtained and so on. The set of prime numbers obtained that are multiplied to each other to form the bigger number are called the factors.