Simplify The Expression:${ 25 \sqrt{11} - \sqrt{11} = }$

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Introduction

Simplifying algebraic expressions is a crucial skill in mathematics, and it's essential to understand the rules and techniques involved. In this article, we will focus on simplifying the expression $25 \sqrt{11} - \sqrt{11}$ using basic algebraic manipulations. We will break down the expression into smaller parts, apply the rules of arithmetic operations, and finally simplify the expression to its simplest form.

Understanding the Expression

The given expression is $25 \sqrt{11} - \sqrt{11}$. This expression involves the subtraction of two terms, where the first term is $25 \sqrt{11}$ and the second term is $\sqrt{11}$. To simplify this expression, we need to apply the rules of arithmetic operations, specifically the distributive property and the properties of radicals.

Applying the Distributive Property

The distributive property states that for any real numbers $a$, $b$, and $c$, the following equation holds:

$a(b + c) = ab + ac$

We can apply this property to the given expression by factoring out the common term $\sqrt{11}$ from both terms:

$25 \sqrt{11} - \sqrt{11} = \sqrt{11}(25 - 1)$

Simplifying the Expression

Now that we have factored out the common term $\sqrt{11}$, we can simplify the expression further by evaluating the expression inside the parentheses:

$25 - 1 = 24$

So, the expression becomes:

$\sqrt{11}(24)$

Final Simplification

The expression $\sqrt{11}(24)$ can be simplified further by multiplying the two terms:

$\sqrt{11}(24) = 24\sqrt{11}$

Therefore, the simplified expression is $24\sqrt{11}$.

Conclusion

In this article, we simplified the expression $25 \sqrt{11} - \sqrt{11}$ using basic algebraic manipulations. We applied the distributive property and the properties of radicals to simplify the expression to its simplest form, which is $24\sqrt{11}$. This example demonstrates the importance of understanding the rules and techniques involved in simplifying algebraic expressions.

Frequently Asked Questions

• Q: What is the simplified form of the expression $25 \sqrt{11} - \sqrt{11}$? A: The simplified form of the expression is $24\sqrt{11}$.
• Q: How do you simplify an expression involving radicals? A: To simplify an expression involving radicals, you can apply the distributive property and the properties of radicals.
• Q: What is the distributive property? A: The distributive property states that for any real numbers $a$, $b$, and $c$, the following equation holds: $a(b + c) = ab + ac$.

Additional Resources

• For more information on simplifying algebraic expressions, visit the Khan Academy website.
• For a comprehensive guide to algebra, visit the Mathway website.
• For practice problems and exercises, visit the IXL website.

Final Thoughts

Simplifying algebraic expressions is a crucial skill in mathematics, and it's essential to understand the rules and techniques involved. By applying the distributive property and the properties of radicals, we can simplify complex and arrive at their simplest form. With practice and patience, you can master the art of simplifying algebraic expressions and become proficient in mathematics.

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Introduction

In our previous article, we simplified the expression $25 \sqrt{11} - \sqrt{11}$ using basic algebraic manipulations. We applied the distributive property and the properties of radicals to simplify the expression to its simplest form, which is $24\sqrt{11}$. In this article, we will provide a Q&A section to address common questions and concerns related to simplifying algebraic expressions.

Q&A

Q: What is the simplified form of the expression $25 \sqrt{11} - \sqrt{11}$?

A: The simplified form of the expression is $24\sqrt{11}$.

Q: How do you simplify an expression involving radicals?

A: To simplify an expression involving radicals, you can apply the distributive property and the properties of radicals.

Q: What is the distributive property?

A: The distributive property states that for any real numbers $a$, $b$, and $c$, the following equation holds: $a(b + c) = ab + ac$.

Q: Can you provide an example of how to apply the distributive property to simplify an expression?

A: Yes, consider the expression $3(2x + 5)$. To simplify this expression, we can apply the distributive property as follows:

$3(2x + 5) = 3(2x) + 3(5)$

$= 6x + 15$

Q: How do you simplify an expression involving multiple radicals?

A: To simplify an expression involving multiple radicals, you can apply the properties of radicals, such as the product rule and the quotient rule.

Q: What is the product rule for radicals?

A: The product rule for radicals states that for any real numbers $a$ and $b$, the following equation holds:

$\sqrt{ab} = \sqrt{a} \cdot \sqrt{b}$

Q: Can you provide an example of how to apply the product rule to simplify an expression?

A: Yes, consider the expression $\sqrt{12x}$. To simplify this expression, we can apply the product rule as follows:

$\sqrt{12x} = \sqrt{12} \cdot \sqrt{x}$

$= 2\sqrt{3x}$

Q: How do you simplify an expression involving a radical and a coefficient?

A: To simplify an expression involving a radical and a coefficient, you can apply the properties of radicals and the distributive property.

Q: Can you provide an example of how to simplify an expression involving a radical and a coefficient?

A: Yes, consider the expression $3\sqrt{2}$. To simplify this expression, we can apply the distributive property as follows:

$3\sqrt{2} = 3 \cdot \sqrt{2}$

$= 3\sqrt{2}$

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

A: Some common mistakes to avoid when simplifying algebraic expressions include:

• Not applying the distributive property correctly
• Not using the properties of radicals correctly
• Not simplifying the expression to its simplest form

Conclusion

In this article, we provided a Q&A section to address common questions and concerns related to simplifying algebraic. We covered topics such as the distributive property, the product rule for radicals, and simplifying expressions involving multiple radicals. By understanding these concepts and applying them correctly, you can simplify complex algebraic expressions and arrive at their simplest form.

Additional Resources

• For more information on simplifying algebraic expressions, visit the Khan Academy website.
• For a comprehensive guide to algebra, visit the Mathway website.
• For practice problems and exercises, visit the IXL website.

Final Thoughts

Simplifying algebraic expressions is a crucial skill in mathematics, and it's essential to understand the rules and techniques involved. By applying the distributive property, the product rule for radicals, and the properties of radicals, you can simplify complex and arrive at their simplest form. With practice and patience, you can master the art of simplifying algebraic expressions and become proficient in mathematics.