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# Square Root of Fractions

Finding the square root of fractions follows the same process as finding the square root of whole numbers or decimals.

• Square Root of Fractions
• Solved Examples
• FAQs

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## Square Root of Fractions

Finding the square root of fractions follows the same process as finding the square root of whole numbers or decimals. The only difference is that the fraction needs to be simplified first before finding the square root.

Here’s the general process for finding the square root of a fraction:

Step 1: Simplify the fraction if possible.

Step 2: Find the square root of the numerator and the denominator separately.

Step 3: Simplify the resulting fraction, if necessary. Let’s look at some examples:

Example 1: Find the square root of 4/9.

Solution:

Step 1: The fraction 4/9 is already in its simplest form.

Step 2: Find the square root of the numerator and denominator separately: √4/√9 = 2/3.

Step 3: The resulting fraction is already in its simplest form.

Example 2: Find the square root of 16/25.

Solution:

Step 1: Simplify the fraction: 16/25 = 4/5.

Step 2: Find the square root of the numerator and denominator separately: √4/√5 = 2/√5.

Step 3: Simplify the fraction by multiplying the numerator and denominator by √5: 2/√5 × √5/√5 = 2√5/5.

Example 3: Find the square root of 3/8, correct to two decimal places.

Solution:

Step 1: Simplify the fraction: 3/8 cannot be simplified further.

Step 2: Find the square root of the numerator and denominator separately: √3/√8 = √3/(√4 × √2) = √3/(2√2).

Step 3: Rationalize the denominator by multiplying the numerator and denominator by the conjugate of the denominator: √3/(2√2) × (√2/√2) = √6/(2√4).

Step 4: Simplify the expression: √6/(2√4) = √6/(2 × 2) = √6/4.

Step 5: Round the answer to two decimal places: √3/8 ≈ 0.62.

Note that when simplifying the fraction, it’s important to simplify it as much as possible to avoid unnecessarily complicated calculations.

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Solved Examples

Example 1: Find the square root of 9/16.

Solution:

Step 1: Simplify the fraction: 9/16 can be simplified to 3/4.

Step 2: Find the square root of the numerator and denominator separately: √3/√4 = √3/2.

Step 3: The resulting fraction is already in its simplest form.

Example 2: Find the square root of 1/25.

Solution:

Step 1: The fraction 1/25 is already in its simplest form.

Step 2: Find the square root of the numerator and denominator separately: √1/√25 = 1/5.

Step 3: The resulting fraction is already in its simplest form.

Example 3: Find the square root of 7/18, correct to two decimal places.

Solution:

Step 1: The fraction 7/18 cannot be simplified further.

Step 2: Find the square root of the numerator and denominator separately: √7/√18 = √(7/18).

Step 3: To simplify the fraction, we need to multiply both the numerator and denominator by a fraction that will eliminate the square root in the denominator. To do this, we can multiply by the square root of 2/2: √(7/18) × √2/√2 = √14/6.

Step 4: Round the answer to two decimal places: √7/18 ≈ 0.62.

Answer: √7/18 ≈ 0.62 (rounded to two decimal places).

## FAQS

##### What is the general process for finding the square root of a fraction?

The general process is to simplify the fraction first, then find the square root of the numerator and denominator separately, and simplify the resulting fraction if necessary.

##### Can fractions with irrational denominators have simplified square roots?

Yes, fractions with irrational denominators can have simplified square roots. For example, √(2/5) can be simplified to √2/√5.

##### How can I simplify the square root of a fraction?

To simplify the square root of a fraction, you need to eliminate any square roots in the denominator. To do this, you can multiply both the numerator and denominator by a fraction that will eliminate the square root in the denominator.

##### Can the square root of a fraction be a whole number?

Yes, the square root of a fraction can be a whole number. For example, √1/4 = 1/2.

##### What should I do if the square root of a fraction is an irrational number?

If the square root of a fraction is an irrational number, you can leave the answer in simplified radical form or approximate it as a decimal. 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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