Square Root of 1.43

The square root is the inverse of the square of a number. 1.43 is not a perfect square. The square root of 1.43 is expressed in both radical and exponential form. In radical form, it is expressed as √1.43, whereas in exponential form, it is (1.43)^(1/2). The value of √1.43 is approximately 1.19523, 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:

• Long division method
   
• Approximation method

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 1.43, we treat it as 1.43.

Step 2: Now we need to find n whose square is closest to 1. We can say n as ‘1’ because 1 × 1 is lesser than or equal to 1. Now the quotient is 1, and after subtracting 1 - 1, the remainder is 0.

Step 3: Now let us bring down 43, which is the new dividend. Add the old divisor with the same number 1 + 1 to get 2, which will be our new divisor.

Step 4: The new divisor will be 2n, and we need to find the value of n.

Step 5: The next step is finding 2n × n ≤ 43. Let us consider n as 1, now 2 × 1 × 1 = 2.

Step 6: Subtract 2 from 43; the difference is 41, and the quotient is 1.

Step 7: Since the dividend has no more digits, 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 4100.

Step 8: Now we need to find the new divisor that fits. Let us consider 21.9 because 219 × 9 = 1971.

Step 9: Subtracting 1971 from 4100, we get the result 2129.

Step 10: Continue this process until we have the desired precision.

The quotient so far is approximately 1.19.

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 1.43 using the approximation method.

Step 1: Now we have to find the closest perfect squares of √1.43. The smallest perfect square less than 1.43 is 1 and the largest perfect square greater than 1.43 is 4. √1.43 falls somewhere between 1 and 2.

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 (1.43 - 1) ÷ (4 - 1) = 0.1433. 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 1 + 0.1433 ≈ 1.1953,

so the square root of 1.43 is approximately 1.1953.

• Square root: A square root is the inverse of a square. For example, 1.2^2 = 1.44, and the inverse of the square is the square root, that is, √1.44 = 1.2.

• 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.

• Decimal: If a number has a whole number and a fraction in a single number, then it is called a decimal. For example, 1.43, 2.56, and 3.78 are decimals.

• Long division method: A method used to find the square root of a number by dividing it into parts and estimating.

• Approximation method: A technique to find a rough estimate of a number's square root by comparing it to nearby perfect squares.