Square Root of 16/49: Simplified Explanation and Calculation

The square root of a fraction can be found by taking the square root of the numerator and the denominator separately.

Steps to Simplify

1. Identify the numerator and the denominator in the fraction.
2. Take the square root of the numerator.
3. Take the square root of the denominator.
4. Simplify the resulting fraction if possible.

Calculation

Given the fraction: $$

16
49

The square root of the numerator (16) is 4, and the square root of the denominator (49) is 7. Thus:

$$


16
49


=

4
7

The decimal form of $$

4
7

is approximately 0.5714.

Additional Examples

Summary

• The square root of $\frac{16}{49}$ is $\frac{4}{7}$.
• The decimal form is approximately 0.5714.

The square root of 16/49 is a simple yet interesting mathematical problem. To find the square root of this fraction, we can simplify it by finding the square root of both the numerator (16) and the denominator (49) separately.

1. First, rewrite the fraction under a single square root: \( \sqrt{\frac{16}{49}} \).
2. Next, separate the square root into the numerator and the denominator: \( \frac{\sqrt{16}}{\sqrt{49}} \).
3. Simplify each part individually:
   • The square root of 16 is 4: \( \sqrt{16} = 4 \).
   • The square root of 49 is 7: \( \sqrt{49} = 7 \).
4. Combine these results to obtain the simplified form: \( \frac{4}{7} \).

Thus, the square root of 16/49 is \( \frac{4}{7} \). This simplification shows the ease with which fractions can be handled when broken down into their basic components.

Calculating the square root of the fraction \( \frac{16}{49} \) is straightforward when broken down into simple steps. Here’s a detailed guide:

1. Start by writing the fraction under a single square root: \[ \sqrt{\frac{16}{49}} \]
2. Separate the square root into the numerator and the denominator: \[ \frac{\sqrt{16}}{\sqrt{49}} \]
3. Find the square root of the numerator (16) and the denominator (49) individually:
   • The square root of 16 is 4: \[ \sqrt{16} = 4 \]
   • The square root of 49 is 7: \[ \sqrt{49} = 7 \]
4. Combine the simplified numerator and denominator to get the final result: \[ \frac{4}{7} \]

Thus, the square root of \( \frac{16}{49} \) simplifies neatly to \( \frac{4}{7} \). This method of simplifying fractions by separating and simplifying each component individually makes it easier to understand and solve similar problems.

Understanding the square root of a fraction involves breaking down the problem into simpler parts. Here is a detailed example using the fraction \( \frac{16}{49} \).

1. Start by writing the fraction under a single square root: \[ \sqrt{\frac{16}{49}} \]
2. Separate the square root into the numerator and the denominator: \[ \sqrt{\frac{16}{49}} = \frac{\sqrt{16}}{\sqrt{49}} \]
3. Find the square root of the numerator:
   • The square root of 16 is 4: \[ \sqrt{16} = 4 \]
4. Find the square root of the denominator:
   • The square root of 49 is 7: \[ \sqrt{49} = 7 \]
5. Combine these results to get the simplified form: \[ \frac{\sqrt{16}}{\sqrt{49}} = \frac{4}{7} \]

Thus, the square root of \( \frac{16}{49} \) simplifies to \( \frac{4}{7} \). This method shows how breaking down the problem into smaller steps can make the calculation easier and more understandable.

The square root of a fraction can also be expressed in decimal form. For the fraction $$

16
49

, its square root is $$


16
49


, which simplifies to
$$

4
7

. In decimal form, this is approximately 0.5714.

Here are the steps to convert the simplified fraction to its decimal form:

1. Identify the simplified fraction: $\frac{4}{7}$
2. Divide the numerator by the denominator: 4 ÷ 7 = 0.5714285714285714...
3. Round to the desired decimal places. Common practice is to round to four decimal places: 0.5714.

Thus, the decimal form of the square root of
$$

16
49


is approximately 0.5714.

Understanding the concept of finding the square root of fractions can be further solidified by examining more examples. Here, we will explore various fractions and their square roots, detailing each step to ensure clarity.

• Consider the fraction \(\frac{9}{16}\). To find its square root, rewrite it as \(\sqrt{\frac{9}{16}} = \frac{\sqrt{9}}{\sqrt{16}}\). Since \(\sqrt{9} = 3\) and \(\sqrt{16} = 4\), we have \(\sqrt{\frac{9}{16}} = \frac{3}{4}\).

• Next, take \(\frac{25}{36}\). The square root is \(\sqrt{\frac{25}{36}} = \frac{\sqrt{25}}{\sqrt{36}}\). With \(\sqrt{25} = 5\) and \(\sqrt{36} = 6\), the simplified form is \(\frac{5}{6}\).

• For a more complex example, consider \(\frac{49}{64}\). The square root is calculated as \(\sqrt{\frac{49}{64}} = \frac{\sqrt{49}}{\sqrt{64}}\). Since \(\sqrt{49} = 7\) and \(\sqrt{64} = 8\), we get \(\frac{7}{8}\).

• Let's look at \(\frac{81}{100}\). To find its square root, we have \(\sqrt{\frac{81}{100}} = \frac{\sqrt{81}}{\sqrt{100}}\). Here, \(\sqrt{81} = 9\) and \(\sqrt{100} = 10\), giving us \(\frac{9}{10}\).

Through these examples, it becomes evident that finding the square root of a fraction involves taking the square root of the numerator and the denominator separately. This method can be applied to any fraction, simplifying the process and providing accurate results.