Square Root of 961

The square root is the inverse of the square of the number. 961 is a perfect square. The square root of 961 is expressed in both radical and exponential form. In the radical form, it is expressed as √961, whereas (961)^(1/2) in the exponential form. √961 = 31, which is a rational number because it can be expressed in the form of p/q, where p and q are integers and q ≠ 0.

The prime factorization method is used for perfect square numbers. Since 961 is a perfect square number, the prime factorization method is applicable. Let us now learn the following methods:

1. Prime factorization method
2. Long division method
3. Approximation method

The product of prime factors is the prime factorization of a number. Now let us look at how 961 is broken down into its prime factors.

Step 1: Finding the prime factors of 961 Breaking it down, we get 31 x 31.

Step 2: Now we found out the prime factors of 961. Since 961 is a perfect square, the digits of the number can be grouped in pairs.

Therefore, the square root of 961 using prime factorization is possible and is equal to 31.

The long division method is particularly used for both perfect and non-perfect square numbers. Let us now learn how to find the square root using the long division method, step by step.

Step 1: To begin with, we need to group the numbers from right to left. In the case of 961, we need to group it as 61 and 9.

Step 2: Now we need to find a number n whose square is less than or equal to 9. We can say n is '3' because 3 x 3 = 9. Now the quotient is 3.

Step 3: Now let us bring down 61, which is the new dividend. Add the old divisor with the same number 3 + 3 to get 6, which will be our new divisor.

Step 4: Multiply the new divisor 6 by n to find the value of n.

Step 5: The next step is finding 6n x n ≤ 61. Let us consider n as 1, now 6 x 1 x 1 = 61.

Step 6: Subtract 61 from 61, the remainder is 0.

So the square root of √961 is 31.

The approximation method is another method for finding square roots. It is an easy method to find the square root of a given number. Now let us learn how to find the square root of 961 using the approximation method.

Step 1: Now we have to find the closest perfect squares of √961. The closest perfect squares are 900 and 1024. √961 falls exactly at 31.

Step 2: Since 961 is a perfect square, the square root is exactly 31 without the need for further approximation.

• Square root: A square root is the inverse of a square. Example: 5² = 25 and the inverse of the square is the square root, that is √25 = 5.

• Rational number: A rational number is a number that can be written in the form of p/q, where q is not equal to zero and p and q are integers.

• Perfect square: A perfect square is a number that is the square of an integer. For example, 961 is a perfect square.

• Prime number: A prime number is a number greater than 1 that has no positive divisors other than 1 and itself.

• Long division method: A method used to find the square root of both perfect and non-perfect squares by dividing and approximating.