Square Root of 7.2

The square root is the inverse of the square of the number. 7.2 is not a perfect square. The square root of 7.2 is expressed in both radical and exponential form. In the radical form, it is expressed as √7.2, whereas (7.2)^(1/2) in the exponential form. √7.2 ≈ 2.68328, 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:

• 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 7.2 is broken down into its prime factors.

Step 1: Finding the prime factors of 7.2 Breaking it down, we get 2 x 3.6, and further 3.6 can be broken down into 2 x 1.8, and 1.8 into 2 x 0.9, which is not applicable for prime factorization as it involves non-integers.

Step 2: Since 7.2 is not a perfect square, calculating it using prime factorization is impractical.

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. Since 7.2 is a decimal, we consider 72 as the number to work with initially.

Step 2: Find a number whose square is less than or equal to 7. The number is 2 because 2 x 2 = 4.

Step 3: Subtract 4 from 7 to get the remainder 3, and bring down the next pair, 20, making the new dividend 320.

Step 4: Double the divisor 2 to get 4. Now, we need to find a number that, when added to 40 and multiplied by itself, is less than or equal to 320.

Step 5: The number is 6 because 46 x 6 = 276, which is less than 320.

Step 6: Subtract 276 from 320 to get the remainder 44.

Step 7: Add a decimal point and bring down 00, making the new dividend 4400.

Step 8: Double the current quotient (26) to get 52. Find a number that, when added to 520 and multiplied by itself, is less than or equal to 4400.

Step 9: The number is 8 because 528 x 8 = 4224.

Step 10: Subtract 4224 from 4400 to get the remainder 176.

Step 11: Continue doing these steps until we get two numbers after the decimal point.

So the square root of √7.2 ≈ 2.683.

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 7.2 using the approximation method.

Step 1: Find the closest perfect squares of √7.2.

The smallest perfect square less than 7.2 is 4 (2^2), and the largest perfect square more than 7.2 is 9 (3^2). √7.2 falls between 2 and 3.

Step 2: Apply the linear interpolation formula to approximate the square root: (Given number - smallest perfect square) ÷ (greater perfect square - smallest perfect square) (7.2 - 4) ÷ (9 - 4) = 3.2 ÷ 5 = 0.64 Add this decimal value to the smaller integer square root: 2 + 0.64 = 2.64

So, the approximate square root of 7.2 is 2.68.

• Square root: The square root is the inverse of squaring a number. For example, 4² = 16, and the inverse is the square root, √16 = 4.

• Irrational number: An irrational number cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.

• Decimal number: A number that contains a fractional part separated from the integer part by a decimal point, like 7.2, 3.14, or 0.001.

• Long division method: A method used for finding the square root of non-perfect squares by dividing the number into pairs and finding successive digits of the root.

• Approximation method: A technique for estimating the value of a square root by finding the nearest perfect squares and using interpolation.