Square Root of 72.25

The square root is the inverse operation of squaring a number. 72.25 is not a perfect square. The square root of 72.25 can be expressed in both radical and exponential form.

In radical form, it is expressed as √72.25, whereas in exponential form, it is expressed as (72.25)^(1/2). The square root of 72.25 is 8.5, which is a rational number because it can be expressed as a fraction, specifically 85/10.

The prime factorization method is typically used for perfect square numbers. However, for non-perfect square numbers, methods such as the long division method and approximation method are preferred. Let's explore these methods:

1. Long division method
2. Approximation method

The long division method is useful for finding the square root of non-perfect squares. Let's learn how to find the square root using this method step by step.

Step 1: Start by pairing the digits from right to left. In 72.25, group as 72 and 25.

Step 2: Find the largest number whose square is less than or equal to 72. This number is 8, because 8 squared is 64. The quotient is 8, and the remainder after subtracting is 72 - 64 = 8.

Step 3: Bring down the next pair of digits, 25, to make 825.

Step 4: Double the quotient (8) to get 16. Find a digit n such that 16n × n is less than or equal to 825. Here, n is 5, as 165 × 5 = 825.

Step 5: Subtract 825 from 825 to get a remainder of 0. The quotient is 8.5.

Thus, the square root of 72.25 is 8.5.

The approximation method is another technique for finding square roots. It is a straightforward method to estimate the square root of a number. Let's find the square root of 72.25 using this approach.

Step 1: Identify the nearest perfect squares around 72.25. The nearest perfect squares are 64 (8^2) and 81 (9^2).

Step 2: Since 72.25 is closer to 64, we estimate the square root is slightly more than 8.

Step 3: Calculate a more precise decimal by interpolation or trial and error. Since 72.25 is exactly 8.5², the square root is exactly 8.5.

So, the square root of 72.25 is 8.5.

• Square root: A square root is a value that, when multiplied by itself, gives the original number. Example: 8.5 × 8.5 = 72.25, so √72.25 = 8.5.

• Rational number: A rational number is any number that can be expressed as the quotient or fraction of two integers, with a non-zero denominator.

• Perfect square: A perfect square is an integer that is the square of an integer. 72.25 is a perfect square because it is 8.5 squared.

• Long division method: A technique used to find the square root of a number by dividing and averaging.

• Decimal: A number that has a whole number and a fractional part separated by a decimal point, such as 8.5.