Square Root of 0.35

The square root is the inverse of the square of the number. 0.35 is not a perfect square. The square root of 0.35 is expressed in both radical and exponential form. In radical form, it is expressed as √0.35, whereas in exponential form it is (0.35)^(1/2). √0.35 ≈ 0.59161, 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 suitable for non-perfect square numbers like 0.35. Instead, 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 find the square root step by step by identifying numbers that come close to the given number's square. Let's see how to find the square root using the long division method:

Step 1: Start grouping the numbers from right to left. For 0.35, consider it as 35 with a decimal point.

Step 2: Find a number whose square is less than or equal to the first part of the number. Here, 5 is the closest, as 5 x 5 = 25.

Step 3: Subtract 25 from 35, leaving a remainder of 10. Bring down two zeros to make it 1000.

Step 4: Double the divisor (5), making it 10, and determine the next digit of the quotient as 9, making the divisor 109.

Step 5: Multiply 109 by 9 to get 981. Subtract this from 1000 to get 19, and then bring down more zeros.

Step 6: Continue the process to get more decimal places.

The quotient will approximate to 0.59161.

The approximation method helps find the square root of a number by estimation. Here’s how to approximate the square root of 0.35:

Step 1: Identify two perfect squares between which 0.35 falls. The closest are 0.25 (0.5²) and 0.36 (0.6²).

Step 2: Use interpolation to approximate: (0.35 - 0.25) / (0.36 - 0.25) = 0.1 / 0.11 ≈ 0.9091

Step 3: Calculate: 0.5 + (0.1 / 0.11) * (0.6 - 0.5) = 0.5 + 0.09091 ≈ 0.591

Thus, the approximate square root of 0.35 is 0.591.

• Square root: A square root is the inverse operation of squaring a number. Example: 0.5² = 0.25 and the inverse square root is √0.25 = 0.5.
   
• Irrational number: An irrational number cannot be written as a simple fraction, such as √0.35, which is approximately 0.59161.
   
• Rational number: A rational number can be expressed as a ratio of two integers. For example, 0.35 = 35/100.
   
• Decimal: A decimal number contains a whole number and a fractional part separated by a decimal point, such as 0.35.
   
• Long division method: A method used to find square roots of non-perfect squares by dividing and averaging numbers systematically.