Square Root of 954

The square root is the inverse of the square of the number. 954 is not a perfect square. The square root of 954 is expressed in both radical and exponential form. In the radical form it is expressed as, √954, whereas (954^)(1/2) in the exponential form. √954 = 30.892, which is an irrational number because it cannot 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. However, the prime factorization method is not used for non-perfect square numbers where long-division method and approximation method are used. 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 954 is broken down into its prime factors.

Step 1: Finding the prime factors of 954 Breaking it down, we get 2 x 3 x 3 x 53: 2¹ x 3² x 53¹

Step 2: Now we found out the prime factors of 954. The second step is to make pairs of those prime factors. Since 954 is not a perfect square, therefore the digits of the number can’t be grouped in pairs.

Therefore, calculating 954 using prime factorization is impossible.

The long division method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. 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 954, we need to group it as 54 and 9.

Step 2: Now we need to find n whose square is 9. We can say n as ‘3’ because 3 x 3 is lesser than or equal to 9. Now the quotient is 3 after subtracting 9-9 the remainder is 0.

Step 3: Now let us bring down 54 which is the new dividend. Add the old divisor with the same number 3 + 3 we get 6 which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 6n as the new divisor, we need to find the value of n.

Step 5: The next step is finding 6n x n ≤ 54 let us consider n as 0, now 6 x 0 x 0 = 0

Step 6: Subtract 54 from 0 the difference is 54, and the quotient is 30.

Step 7: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 5400.

Step 8: Now we need to find the new divisor that is 308 because 308 x 8 = 2464

Step 9: Subtracting 2464 from 5400 we get the result 2936.

Step 10: Now the quotient is 30.8

Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values continue till the remainder is zero.

So the square root of √954 is approximately 30.89

The approximation method is another method for finding the 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 954 using the approximation method.

Step 1: Now we have to find the closest perfect square of √954. The smallest perfect square less than 954 is 900 and the largest perfect square greater than 954 is 961. √954 falls somewhere between 30 and 31.

Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).

Going by the formula (954 - 900) / (961 - 900) = 54 / 61 = 0.8852 Using the formula we identified the decimal point of our square root.

The next step is adding the value we got initially to the decimal number which is 30 + 0.8852 = 30.8852, so the square root of 954 is approximately 30.89.

• Square root: A square root is the inverse of a square. Example: 4² = 16 and the inverse of the square is the square root, that is √16 = 4.

• Irrational number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.

• Principal square root: A number has both positive and negative square roots; however, it is always the positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as a principal square root.

• Prime factorization: Prime factorization is expressing a number as the product of its prime factors.

• Long division method: The long division method is a technique used to find the square root of a number by dividing it into groups and estimating the root step by step.