Square Root of 888

The square root is the inverse of the square of a number. 888 is not a perfect square. The square root of 888 is expressed in both radical and exponential forms. In radical form, it is expressed as √888, whereas (888)^(1/2) in exponential form. √888 ≈ 29.7993, 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, for non-perfect square numbers like 888, the long-division method and approximation method are used. Let us now learn the following methods:

• Prime factorization method
• Long division method
• Approximation method

The product of prime factors is the prime factorization of a number. Now let us look at how 888 is broken down into its prime factors.

Step 1: Finding the prime factors of 888 Breaking it down, we get 2 x 2 x 2 x 3 x 37: 2^3 x 3 x 37

Step 2: Now we found the prime factors of 888. The second step is to make pairs of those prime factors. Since 888 is not a perfect square, the digits of the number can’t be grouped in pairs.

Therefore, calculating √888 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 888, we need to group it as 88 and 8.

Step 2: Now we need to find a number 'n' whose square is 8 or less. We can say n is ‘2’ because 2 x 2 = 4, which is less than 8. Now the quotient is 2, and after subtracting 4 from 8, the remainder is 4.

Step 3: Now let us bring down 88, which is the new dividend. Add the old divisor with the same number: 2 + 2 = 4, which will be our new divisor.

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

Step 5: The next step is finding 4n × n ≤ 488. Let's consider n as 7; now 4 x 7 x 7 = 196.

Step 6: Subtract 196 from 488; the difference is 292, and the quotient is 27.

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 29200.

Step 8: Now we need to find the new divisor that is 279 because 2799 x 9 = 25191.

Step 9: Subtracting 25191 from 29200, we get the result 4009.

Step 10: Now the quotient is 29.7.

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

So the square root of √888 is approximately 29.79.

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 888 using the approximation method.

Step 1: Now we have to find the closest perfect square to √888.

The smallest perfect square less than 888 is 841, and the largest perfect square greater than 888 is 900.

√888 falls somewhere between 29 and 30.

Step 2: Now we need to apply the formula:

(Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).

Using the formula, (888 - 841) ÷ (900 - 841) = 47 ÷ 59 ≈ 0.7966.

Adding this to the smaller perfect square root: 29 + 0.7966 = 29.7966, so the square root of 888 is approximately 29.80.

• Square root: A square root is the inverse of a square. Example: 4^2 = 16, and the inverse of the square is the square root, which 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 zero and p and q are integers.
   
• Principal square root: A number has both positive and negative square roots, but it is usually the positive square root that is used in real-world applications. This is known as the principal square root.
   
• Prime factorization: Prime factorization involves breaking down a number into its prime number components. For example, the prime factorization of 888 is 2^3 x 3 x 37.
   
• Decimal: A decimal is a number with a whole number and a fractional part, represented by digits after a decimal point. For example: 7.86, 8.65, and 9.42 are decimals.