Square root of 97

Approximately ±9.848 is the square root of 97.

In radical form, square root of 97 is written as √97.
 
It is in exponential form (97)^1/2

We can find the square root of 97 through various methods. They are:

i) Prime factorization method

ii) Long division method

iii) Approximation/Estimation method
 

Prime factorization methods find the prime factors of number 97. The smallest prime number is 97 because since it is a prime number, it can’t be factored further.

Step 1: Generate a number that is not a prime number and see if it is identical to 97. As 9 is a prime number, it has no other positive divisors other than 1 and 9 itself.

Step 2: Since 97 cannot be broken down into smaller prime factors, we cannot use the prime factorization method to find the square root of 97.

Therefore from the above calculations we can conclude that the square root of 97 cannot be factored and found by the Prime Factorization method. 

Finding the square root of 97 using the long division method involves:

Step 1: From right to left pair the digits of 97.

Step 2: The largest perfect square less than or equal to 97 is 81 -- the square of 9.

Step 3: Bring down the next pair of 00, and subtract 81 from 97.

97–81 = 16

Bring down 00: 1600

Step 4: Quotient 9 = 9 × 2 = 18

Step 5: What is the largest digit 'X' so that 18X × X ≤ 1600? X = 8 (since 188 x 8 is 1504) is here.

Step 6: Then give 1504 less than 1600, and bring down the next pair of 00.

1600–1504 = 96

Bring down 00: 9600

Step 7: Repeat Steps 4-6,

The quotient 98 = 98 × 2 = 196 double.

You find the next digit 'X' so that 196X × X is less than or equal to 9600. (In this particular case), X = 4 (because 1964 x 4 = 1964 x 4 = 1964 x 4 1964 x 4) 7856).

Subtract and bring down: 9600–7856 = 1744

Continuing the Process:

You can continue this process by finding as many decimal places as you need.

Our calculations above would give you the approximate square root of 97 as 9.84.
 

Steps to find the square root of 97 by approximation method are:

Step 1: We can find the Nearest Perfect Squares: the nearest perfect square is less than 97 (the answer is 81 (9²), the nearest perfect square is greater than 97 (the answer is 100 (10²)).

Step 2: The reason that 9 is closer to 10 and not 81, squared, is that 97 is closer to 100 than 81 because 97 is closer to 100 than 81. The square root of 97 is likely closer to 10 than 9.

Step 3: Divide the Number Divided by the Guess by the Guess, and average that with the Guess.The first guess was 97 over 10; average 10 (our initial guess) and 97 divided by 10.

(10 + 97/10) / 2 = 9.85

Step 4: Repeat Step 3, Average 9.85 and 97 divided by 9.85:

(9.85 + 97/9.85) / 2 ≈ 9.849

As many times as you like you can repeat this process to get a more accurate approximation. 

By application of approximation method, we estimate the square root of 97 approximately 9.849. 
 

• Area of a square: The number of spaces that a square occupies on its sides is called the area of a square. Area of square = Side x Side = Side² 

• Simplification: Making something easier or simpler to understand. 

• Prime number: A natural number greater than 1 which has no positive divisors other than 1 and itself is called a Prime number.