Square Root of 890

The square root is the inverse of the square of the number. 890 is not a perfect square. The square root of 890 is expressed in both radical and exponential form. In the radical form, it is expressed as √890, whereas 890^(1/2) in the exponential form. √890 ≈ 29.8329, 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:

• 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 890 is broken down into its prime factors.

Step 1: Finding the prime factors of 890 Breaking it down, we get 2 x 5 x 89: 2^1 x 5^1 x 89^1

Step 2: Now we found out the prime factors of 890. The second step is to make pairs of those prime factors. Since 890 is not a perfect square, the digits of the number can’t be grouped in pairs.

Therefore, calculating 890 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 890, we need to group it as 90 and 8.

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

Step 3: Now let us bring down 90, which is the new dividend. Add the old divisor with the same number 2 + 2; we get 4, which will be our new divisor.

Step 4: The new divisor will be 4n. We need to find the value of n.

Step 5: The next step is finding 4n x n ≤ 490. Let us consider n as 9. Now 49 x 9 = 441.

Step 6: Subtract 490 from 441; the difference is 49, and the quotient is 29.

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 4900.

Step 8: Now we need to find the new divisor, which is 598, because 598 x 8 = 4784.

Step 9: Subtracting 4784 from 4900, we get the result 116. Step 10: Now the quotient is 29.8

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 √890 is approximately 29.83.

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 890 using the approximation method.

Step 1: Now we have to find the closest perfect square of √890.

The smallest perfect square less than 890 is 841, and the largest perfect square greater than 890 is 900.

√890 falls somewhere between 29 and 30.

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 (890 - 841) / (900 - 841) ≈ 0.83

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 29 + 0.83 = 29.83, so the square root of 890 is approximately 29.83.

• 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, 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.
   
• Perfect square: A perfect square is a number that is the square of an integer. Example: 16 is a perfect square because it is 4^2.
   
• Decimal: A decimal is a number that contains a whole number and a fractional part, represented with a decimal point. Example: 7.86, 8.65, and 9.42 are decimals.
   
• Approximation: Approximation is a method of finding a value that is close enough to the correct answer, usually with some degree of accuracy.