Simplify The Expression: 20 + 8 − 9 5 \sqrt{20} + \sqrt{8} - 9\sqrt{5} 20 ​ + 8 ​ − 9 5 ​

$$

Introduction

Simplifying algebraic expressions is a crucial skill in mathematics, and it requires a deep understanding of various mathematical concepts, including radicals, exponents, and algebraic identities. In this article, we will focus on simplifying the given expression: $\sqrt{20} + \sqrt{8} - 9\sqrt{5}$. We will break down the expression into smaller parts, simplify each part, and then combine them to obtain the final result.

Understanding the Expression

The given expression involves three terms: $\sqrt{20}$, $\sqrt{8}$, and $-9\sqrt{5}$. To simplify the expression, we need to understand the properties of radicals and how to simplify them. A radical is a mathematical expression that represents a number that can be expressed as the product of a whole number and a square root. For example, $\sqrt{20}$ can be written as $\sqrt{4 \times 5}$, which simplifies to $2\sqrt{5}$.

Simplifying the First Term: $\sqrt{20}$

The first term in the expression is $\sqrt{20}$. To simplify this term, we need to find the largest perfect square that divides 20. In this case, the largest perfect square that divides 20 is 4. Therefore, we can write $\sqrt{20}$ as $\sqrt{4 \times 5}$, which simplifies to $2\sqrt{5}$.

Simplifying the Second Term: $\sqrt{8}$

The second term in the expression is $\sqrt{8}$. To simplify this term, we need to find the largest perfect square that divides 8. In this case, the largest perfect square that divides 8 is 4. Therefore, we can write $\sqrt{8}$ as $\sqrt{4 \times 2}$, which simplifies to $2\sqrt{2}$.

Simplifying the Third Term: $-9\sqrt{5}$

The third term in the expression is $-9\sqrt{5}$. This term is already simplified, so we don't need to do anything further.

Combining the Simplified Terms

Now that we have simplified each term, we can combine them to obtain the final result. The expression becomes:

$$2\sqrt{5} + 2\sqrt{2} - 9\sqrt{5}$$

Further Simplification

To further simplify the expression, we can combine like terms. In this case, we have two terms with $\sqrt{5}$: $2\sqrt{5}$ and $-9\sqrt{5}$. We can combine these terms by adding their coefficients:

$$2\sqrt{5} - 9\sqrt{5} = -7\sqrt{5}$$

The expression now becomes:

$$-7\sqrt{5} + 2\sqrt{2}$$

Conclusion

In this article, we simplified the given expression: $\sqrt{20} + \sqrt{8} - 9\sqrt{5}$. We broke down the expression into smaller parts, simplified each part, and then combined them to obtain the final result. The simplified expression is $-7\sqrt{5} + 2\sqrt{2}$.

Final Answer

The final answer is $\boxed{-7\sqrt{5} + 2\sqrt{2}}$.

Related Topics

• Simplifying radicals
• Combining like terms
• Algebraic identities

References

• [1] "Algebra and Trigonometry" by Michael Sullivan
• [2] "Mathematics for the Nonmathematician" by Morris Kline

Further Reading

• [1] "Simplifying Radicals" by Math Open Reference
• [2] "Combining Like Terms" by Khan Academy

Note: The references and further reading sections are not exhaustive and are provided for additional information and resources.

$$

Introduction

In our previous article, we simplified the expression: $\sqrt{20} + \sqrt{8} - 9\sqrt{5}$. We broke down the expression into smaller parts, simplified each part, and then combined them to obtain the final result. In this article, we will answer some frequently asked questions related to the simplification of the expression.

Q&A

Q: What is the largest perfect square that divides 20?

A: The largest perfect square that divides 20 is 4.

Q: How do you simplify $\sqrt{20}$?

A: To simplify $\sqrt{20}$, we can write it as $\sqrt{4 \times 5}$, which simplifies to $2\sqrt{5}$.

Q: What is the largest perfect square that divides 8?

A: The largest perfect square that divides 8 is 4.

Q: How do you simplify $\sqrt{8}$?

A: To simplify $\sqrt{8}$, we can write it as $\sqrt{4 \times 2}$, which simplifies to $2\sqrt{2}$.

Q: What is the final result of the expression: $\sqrt{20} + \sqrt{8} - 9\sqrt{5}$?

A: The final result of the expression is $-7\sqrt{5} + 2\sqrt{2}$.

Q: How do you combine like terms in the expression?

A: To combine like terms in the expression, we can add the coefficients of the terms with the same variable. In this case, we have two terms with $\sqrt{5}$: $2\sqrt{5}$ and $-9\sqrt{5}$. We can combine these terms by adding their coefficients: $2\sqrt{5} - 9\sqrt{5} = -7\sqrt{5}$.

Q: What are some common mistakes to avoid when simplifying radicals?

A: Some common mistakes to avoid when simplifying radicals include:

• Not finding the largest perfect square that divides the number
• Not simplifying the radical correctly
• Not combining like terms correctly

Q: How do you check if the simplification of the expression is correct?

A: To check if the simplification of the expression is correct, we can plug in the simplified expression back into the original expression and see if it is true. In this case, we can plug in $-7\sqrt{5} + 2\sqrt{2}$ back into the original expression and see if it is equal to the original expression.

Conclusion

In this article, we answered some frequently asked questions related to the simplification of the expression: $\sqrt{20} + \sqrt{8} - 9\sqrt{5}$. We provided step-by-step solutions to each question and highlighted some common mistakes to avoid when simplifying radicals.

Final Answer

The final answer is $\boxed{-7\sqrt{5} + 2\sqrt{2}}$.

Related Topics

• Simplifying radicals
• Combining like terms
• Algebraic identities

References

• [1] "Algebra and Trigonometry" by Michael Sullivan
• [2] "Mathematics for the Nonmathematician" by Morris Kline

Further Reading

• [1] "Simplifying Radicals" by Math Open Reference
• [2] "Combining Like Terms" by Khan Academy

Note: The references and further reading sections are not exhaustive and are provided for additional information and resources.