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How do you find the square root 289?

Answer
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Hint: The given question is to find out the square root of the given number. Since 4 is the square of 2. Therefore the square root of 4 is ±2. Hence we can say that square root is nothing but those number if we square the square root number then we get same number back or we can say that square of 2=4
Square root of 4=±2,2

Complete step-by-step answer:
The given question is to find out the square root of the given number. Square of any number means to multiply that number with itself and hence the number obtained is known as square of the number. On the other hand if we do the square root of the obtained number we get the same number twice but with opposite signs, One is positive and other is negative. Herein the given question, we have to find out the square root of the given number which is 289
Here, we have to find out the square root of 289.
We will find out the square root of 289 by prime factorization method. Prime factorization method is the method in which we make the possible smallest factors of the given number and from them,and when we multiply the factors , we get the same number again.
Here we have to find out the square root of 289..
Since 289 is divisible by 17 only means from 2 to 16,289 is not divisible by any number and 289, on divided by 17, left with 17. Also 17 is divisible by 17, therefore we get the 2 factors of 289 which are 17 and 17.
Now , square root of 289 is 289
And we can write 289 as 17×17
Because these are the factors of 289
So, 289=17×17
Inside the square root, twice 17 becomes 17 if we take 17 out of the square root.
Therefore we get
289=17
Hence square root of 289 is 17

Note: If we take square root on both sides we get
(289)2=(17)2
In left side square root and square gets cancel and we get
289=289
Because square of 17 is 289 and we also know square of 2 is 4 and square root of 4 is 2 and 2 because if we take square of 2 and (2), we get 4. Therefore square root of 4 is 2 and 2.
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