Square Root of 16/36

The square root is the inverse of the square of a number. 16/36 is a perfect square fraction. The square root of 16/36 is expressed in both radical and exponential form. In the radical form, it is expressed as √(16/36), whereas (16/36)^(1/2) in the exponential form. √(16/36) = 2/3, 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. Since 16/36 is a perfect square fraction, we can use the prime factorization method to find its square root. 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 16/36 is broken down into its prime factors.

Step 1: Finding the prime factors of 16 and 36 16 can be broken down into 2 x 2 x 2 x 2, which is 2^4. 36 can be broken down into 2 x 2 x 3 x 3, which is 2^2 x 3^2.

Step 2: Now we found out the prime factors of 16 and 36. Since both numbers are perfect squares, we can find the square root easily. √(16/36) = √(2^4 / 2^2 x 3^2) = √(2^2 / 3^2) = 2/3, as both the numerator and denominator can be paired perfectly.

The long division method is typically used for non-perfect square numbers, but it can also be applied to perfect square fractions for verification. Here’s how you can find the square root of 16/36 using the long division method:

Step 1: Divide 16 by 36, which simplifies to 0.4444...

Step 2: Find the square root of 0.4444... using long division:

Step 3: Group the numbers from right to left in pairs, here we start with 0.44.

Step 4: Find a number whose square is less than or equal to 44. In this case, 6^2 = 36.

Step 5: Subtract 36 from 44, giving a remainder of 8. Bring down two zeroes, making it 800.

Step 6: Doubling the result 6, we get 12. Find the next digit in the result, making it 12x, where x is chosen to fit 800.

Step 7: Continue the process to get the decimal approximation, which will eventually lead you to 0.6666...

Approximation method is another technique for finding square roots, particularly useful for verifying results. Here is how we approximate the square root of 16/36:

Step 1: Recognize that 16/36 simplifies to 4/9, which are both perfect squares.

Step 2: Calculate the square roots: √16 = 4 and √36 = 6.

Step 3: Therefore, the square root of 16/36 is 4/6, which simplifies to 2/3. Thus, √(16/36) = 2/3, confirming the exact value.

• Square root: A square root is the inverse of a square. For example: 4^2 = 16, and the inverse of the square is the square root, that is, √16 = 4.

• Rational number: A rational number is a number that can be written in the form of p/q, where p and q are integers and q ≠ 0.

• Perfect square: A perfect square is an integer that is the square of an integer. For example, 16 is a perfect square because it equals 4^2.

• Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 36 is 2^2 x 3^2.

• Fraction: A fraction represents a part of a whole or any number of equal parts. It is represented as p/q, where p is the numerator and q is the denominator.