Simplify The Expression: 112 + 28 \sqrt{112} + \sqrt{28} 112 ​ + 28 ​

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Introduction

In mathematics, simplifying expressions is a crucial skill that helps us solve problems efficiently and accurately. When dealing with square roots, it's essential to simplify the expression to make it easier to work with. In this article, we will simplify the expression $\sqrt{112} + \sqrt{28}$ using various techniques.

Understanding the Expression

The given expression is $\sqrt{112} + \sqrt{28}$. To simplify this expression, we need to understand the properties of square roots. The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4, because 4 multiplied by 4 equals 16.

Breaking Down the Numbers

To simplify the expression, we need to break down the numbers inside the square roots. We can start by finding the prime factors of 112 and 28.

Prime Factors of 112

The prime factors of 112 are 2, 2, 2, 2, 7. We can write this as $2^4 \cdot 7$.

Prime Factors of 28

The prime factors of 28 are 2, 2, 7. We can write this as $2^2 \cdot 7$.

Simplifying the Square Roots

Now that we have the prime factors of 112 and 28, we can simplify the square roots.

Simplifying $\sqrt{112}$

We can rewrite $\sqrt{112}$ as $\sqrt{2^4 \cdot 7}$. Using the property of square roots, we can simplify this as $2^2 \cdot \sqrt{7}$, which equals $4\sqrt{7}$.

Simplifying $\sqrt{28}$

We can rewrite $\sqrt{28}$ as $\sqrt{2^2 \cdot 7}$. Using the property of square roots, we can simplify this as $2\sqrt{7}$.

Combining the Simplified Expressions

Now that we have simplified the individual square roots, we can combine them to get the final expression.

$\sqrt{112} + \sqrt{28} = 4\sqrt{7} + 2\sqrt{7}$

Combining Like Terms

We can combine the like terms in the expression by adding the coefficients of the square roots.

$4\sqrt{7} + 2\sqrt{7} = 6\sqrt{7}$

Conclusion

In this article, we simplified the expression $\sqrt{112} + \sqrt{28}$ using various techniques. We broke down the numbers inside the square roots, found their prime factors, and simplified the square roots. Finally, we combined the simplified expressions and combined like terms to get the final answer. The simplified expression is $6\sqrt{7}$.

Frequently Asked Questions

• What is the simplified expression of $\sqrt{112} + \sqrt{28}$?
• How do we simplify square roots?
• What are the prime factors of 112 and 28?

Final Answer

The final answer is $\boxed{6\sqrt{7}}$.

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Introduction

In our previous article, we simplified the expression $\sqrt{112} + \sqrt{28}$ using various techniques. In this article, we will answer some frequently asked questions related to the simplification of the expression.

Q&A

Q1: What is the simplified expression of $\sqrt{112} + \sqrt{28}$?

A1: The simplified expression of $\sqrt{112} + \sqrt{28}$ is $6\sqrt{7}$.

Q2: How do we simplify square roots?

A2: To simplify square roots, we need to find the prime factors of the number inside the square root. We can then use the property of square roots to simplify the expression.

Q3: What are the prime factors of 112 and 28?

A3: The prime factors of 112 are 2, 2, 2, 2, 7, which can be written as $2^4 \cdot 7$. The prime factors of 28 are 2, 2, 7, which can be written as $2^2 \cdot 7$.

Q4: How do we combine like terms in the expression?

A4: To combine like terms in the expression, we need to add the coefficients of the square roots. For example, in the expression $4\sqrt{7} + 2\sqrt{7}$, we can combine the like terms by adding the coefficients, which gives us $6\sqrt{7}$.

Q5: What is the property of square roots that we used to simplify the expression?

A5: The property of square roots that we used to simplify the expression is $\sqrt{a^2 \cdot b} = a\sqrt{b}$. We used this property to simplify the expressions $\sqrt{112}$ and $\sqrt{28}$.

Q6: Can we simplify the expression further?

A6: No, we cannot simplify the expression further. The simplified expression $6\sqrt{7}$ is the simplest form of the expression.

Additional Tips and Tricks

• When simplifying square roots, make sure to find the prime factors of the number inside the square root.
• Use the property of square roots to simplify the expression.
• Combine like terms in the expression by adding the coefficients of the square roots.
• Check if the expression can be simplified further.

Conclusion

In this article, we answered some frequently asked questions related to the simplification of the expression $\sqrt{112} + \sqrt{28}$. We provided detailed answers to each question and also included some additional tips and tricks to help you simplify square roots.

Frequently Asked Questions (FAQs)

• What is the simplified expression of $\sqrt{112} + \sqrt{28}$?
• How do we simplify square roots?
• What are the prime factors of 112 and 28?
• How do we combine like terms in the expression?
• What is the property of square roots that we used to simplify the expression?
• Can we simplify the expression further?

Final Answer

The final answer is $\boxed{6\sqrt{7}}$.