Square Root of 110.25

The square root is the inverse of the square of the number. 110.25 is a perfect square, and its square root is expressed in both radical and exponential form.

In the radical form, it is expressed as √110.25, whereas (110.25)^(1/2) in exponential form. √110.25 = 10.5, 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 often used for perfect square numbers, but since 110.25 is a decimal perfect square, other methods like the long-division method and direct calculation can be used. Let us now learn the following methods:

1. Direct calculation method
2. Long division method

Since 110.25 is a perfect square, we can directly calculate its square root. Note that 10.5 × 10.5 = 110.25.

Therefore, √110.25 = 10.5.

The long division method can also be used for determining the square root of decimal numbers. Here's a step-by-step guide:

Step 1: Pair the digits of 110.25 from right to left, giving us 10 and 25.

Step 2: Find a number whose square is less than or equal to 10. The number is 3 because 3 × 3 = 9. Subtract 9 from 10, leaving a remainder of 1.

Step 3: Bring down the next pair, 25, making it 125. Double the previous quotient (3), which gives 6.

Step 4: Find a number n such that 6n × n is less than or equal to 125. The number is 2 because 62 × 2 = 124. Subtract 124 from 125, leaving a remainder of 1.

Step 5: Add a decimal point and bring down 00, making it 100.

Step 6: Double the previous quotient (32), getting 64. Find n such that 64n × n is less than or equal to 100. The number is 1 because 641 × 1 = 64.

Step 7: Subtract 64 from 100, leaving a remainder of 36.

Step 8: Repeat the steps until the desired decimal places are achieved.

So, the square root of √110.25 is 10.5.

• Square root: A square root is the inverse of a square. Example: 5² = 25, and the inverse square is the square root, which is √25 = 5.

• Rational number: A rational number can be expressed as a fraction p/q, where p and q are integers and q ≠ 0.

• Perfect square: A number that is the square of an integer. Example: 121 is a perfect square because it is 11².

• Decimal: A number that includes a whole number and a fractional part, separated by a decimal point. Examples: 10.5, 3.14.

• Perimeter: The total length around a two-dimensional shape, calculated by summing the lengths of its sides.