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# Square Root of Decimal

## Square Root of Decimal

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## Square Root of Decimal

To find the square root of a decimal number, you can use the following steps:

Step 1: Write the decimal number in the form of a fraction, with the decimal point as the numerator and 1 followed by as many zeros as there are decimal places as the denominator. For example, the decimal number 2.25 can be written as 225/100.

Step 2: Simplify the fraction by dividing both the numerator and denominator by their greatest common factor. In this example, the greatest common factor of 225 and 100 is 25, so we can simplify the fraction to 9/4.

Step 3: Find the square root of the simplified fraction. In this example, the square root of 9/4 is 3/2.

Step 4: If the original decimal number was not a perfect square, you can round the answer to the desired number of decimal places. In this example, the square root of 2.25 is 1.5.

Therefore, the square root of 2.25 is 1.5.

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Solved Examples

Example 1: Find the square root of 0.25.

Solution:

Step 1: Write 0.25 as a fraction: 0.25 = 25/100.

Step 2: Simplify the fraction: 25/100 = 1/4.

Step 3: Find the square root of 1/4: √(1/4) = 1/2.

Step 4: The square root of 0.25 is 0.5.

Example 2: Find the square root of 6.25.

Solution:

Step 1: Write 6.25 as a fraction: 6.25 = 625/100.

Step 2: Simplify the fraction: 625/100 = 25/4.

Step 3: Find the square root of 25/4: √(25/4) = 5/2.

Step 4: The square root of 6.25 is 2.5.

Example 3: Find the square root of 2.5, correct to two decimal places.

Solution:

Step 1: Write 2.5 as a fraction: 2.5 = 250/100.

Step 2: Simplify the fraction: 250/100 = 5/2.

Step 3: Find the square root of 5/2 using a calculator or approximation method: √(5/2) ≈ 1.58.

Step 4: Round the answer to two decimal places: √2.5 ≈ 1.58.

Answer: √2.5 ≈ 1.58 (rounded to two decimal places).

Example 4: Find the square root of 3. Correct the answer to three decimal places.

Solution:

Step 1: Write 3 as a fraction: 3 = 3000/1000.

Step 2: Simplify the fraction: 3000/1000 = 3/1.

Step 3: Find the square root of 3 using a calculator or approximation method: √3 ≈ 1.732.

Step 4: Round the answer to three decimal places: √3 ≈ 1.732.

Answer: √3 ≈ 1.732 (rounded to three decimal places).

## FAQS

##### Can every decimal number have a square root?

Yes, every non-negative real number has a unique non-negative square root. However, some decimal numbers, like irrational numbers, have an infinite decimal expansion and cannot be expressed as a finite decimal or fraction.

##### Can you find the square root of a negative decimal number?

No, the square root of a negative number is not a real number. It is a complex number.

##### How do I know if the decimal number is a perfect square?

If the decimal number has a finite decimal representation and the last two digits are either 00, 01, 04, 09, 16, 21, 24, 25, 29, 36, 41, 44, 49, 56, 61, 64, 69, 76, 81, or 84, then the number is a perfect square. Otherwise, it is not a perfect square.

##### How many decimal places should I round the answer to when finding the square root of a decimal number?

The number of decimal places to round the answer to depends on the level of precision required in the problem. Typically, the answer is rounded to two or three decimal places.

##### What is the relationship between the square root of a decimal and the square root of its whole number factor?

The square root of a decimal number is equal to the product of the square root of its largest perfect square factor and the square root of the remaining non-perfect square factor. For example, the square root of 18 is equal to the square root of 9 times the square root of 2, which is equal to 3√2.

Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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