Square Root of Fractions

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

Table of Contents:

• Square Root of Fractions
• Solved Examples
• FAQs

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.

Answer: √4/9 = 2/3.

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.

Answer: √16/25 = 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.

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.

Answer: √9/16 = √3/2.

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.

Answer: √1/25 = 1/5.

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

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