Square Root of 0.36

The square root is the inverse of the square of the number. 0.36 is a perfect square. The square root of 0.36 is expressed in both radical and exponential form. In the radical form, it is expressed as √0.36, whereas (0.36)^(1/2) in the exponential form. √0.36 = 0.6, which is a rational number because it can 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, the long-division method and approximation method are used. Let's 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 0.36 is broken down into its prime factors.

Step 1: Convert 0.36 to a fraction: 0.36 = 36/100.

Step 2: Find the prime factors of 36 and 100. 36 = 2 × 2 × 3 × 3 100 = 2 × 2 × 5 × 5

Step 3: Pair the prime factors: (2 × 2) × (3 × 3) and (2 × 2) × (5 × 5).

Step 4: Take the square root of each pair: √(2 × 2) = 2, √(3 × 3) = 3, √(2 × 2) = 2, √(5 × 5) = 5.

Step 5: Therefore, √(36/100) = (2 × 3) / (2 × 5) = 6/10 = 0.6.

The long division method is particularly used for non-perfect square numbers. However, it can also be used for decimals. Let us now learn how to find the square root using the long division method, step by step.

Step 1: Write 0.36 as 36/100 and set up the division for 36.

Step 2: Find a number that, when squared, gives 36. We know 6 × 6 = 36, so the quotient is 6.

Step 3: Since there are two decimal places in 0.36, the decimal point in the quotient will be placed after one digit, giving us 0.6.

So, the square root of √0.36 is 0.6.

The approximation method is another method for finding the 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 0.36 using the approximation method.

Step 1: Identify the perfect squares closest to 0.36. The perfect squares are 0.25 (0.5 × 0.5) and 1 (1 × 1).

Step 2: Since 0.36 is between 0.25 and 1, the square root will be between 0.5 and 1.

Step 3: 0.36 is closer to 0.25, so we try 0.6. 0.6 × 0.6 = 0.36.

Thus, the square root of 0.36 is 0.6.

• Square root: A square root is the inverse of a square. Example: 0.6² = 0.36 and the inverse of the square is the square root, that is √0.36 = 0.6.
   
• Rational number: A rational number is a number that can 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. For example, 0.36 is a perfect square because it is 0.6^2.
   
• Decimal: If a number has a whole number and a fraction in a single number, then it is called a decimal. For example, 0.36 is a decimal.
   
• Principal square root: A number has both positive and negative square roots; however, it is always the positive square root that has more prominence due to its uses in the real world. That is why it is also known as the principal square root.