Square Root of 63

The square root is the inverse of the square of the number. 63 is not a perfect square. The square root of 63 is expressed in both radical and exponential form.

In the radical form, it is expressed as √63, whereas (63)^(1/2) in the exponential form. √63 ≈ 7.93725, 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 the 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 63 is broken down into its prime factors.

Step 1: Finding the prime factors of 63 Breaking it down, we get 3 x 3 x 7: 3^2 x 7

Step 2: Now we found out the prime factors of 63. The second step is to make pairs of those prime factors. Since 63 is not a perfect square, the digits of the number can’t be grouped in pairs.

Therefore, calculating 63 using prime factorization is not exact.

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 63, we need to group it as 63.

Step 2: Now we need to find n whose square is less than or equal to 63. We can say n as ‘7’ because 7 x 7 = 49 which is less than 63. Now the quotient is 7 after subtracting 49 from 63 the remainder is 14.

Step 3: Add the old divisor with the same number 7 + 7 = 14, which will be our new divisor.

Step 4: Bring down two zeros to make the dividend 1400.

Step 5: The new divisor will be 14n, and we need to find n such that 14n x n ≤ 1400. Let's take n as 9, now 149 x 9 = 1341.

Step 6: Subtract 1341 from 1400 to get the remainder of 59, and the quotient becomes 7.9.

Step 7: Continue with these steps until you reach the desired decimal places.

So the square root of √63 ≈ 7.937.

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 63 using the approximation method.

Step 1: Now we have to find the closest perfect squares around √63. The smallest perfect square less than 63 is 49, and the largest perfect square more than 63 is 64. √63 falls somewhere between 7 and 8.

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

Using the formula (63 - 49) / (64 - 49) = 0.9333 Using the formula, we identified the decimal point of our square root.

square root of 63eger part, which is 7, to the decimal number, making it 7 + 0.9333 ≈ 7.9333, so the square root of 63 is approximately 7.937.]


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• Square root: A square root is a value that, when multiplied by itself, gives the original number. Example: √64 = 8 because 8 x 8 = 64.

• Irrational number: An irrational number is a number that cannot be expressed as a simple fraction; its decimal form is non-repeating and non-terminating.

• Approximation: The process of finding a value that is close to the exact value is known as approximation.

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

• Long division method: A method used to divide numbers to find the square root of a non-perfect square by approximating the decimal values.