Question

How do you find the square root of 169?

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 know that 169 is a perfect square. We can find the square root of 169 using factors of 169.

Complete step-by-step answer:
Given, square root of 169.
That is, \[\sqrt {169} \]
169 can be factorized as,
 \[169 = 1 \times 13 \times 13\]
We can see that 13 is multiplied two times, we multiply that we get,
 \[169 = {13^2}\] .
Then,
 \[ \Rightarrow \sqrt {169} = \sqrt {{{13}^2}} \]
We know that when we have square and square root it will cancels out, thus we have:
 \[ = 13\] . This is the exact form. Hence it is a perfect square.
So, the correct answer is “13”.

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. Follow the same procedure for these kinds of problems.