Simplify The Expression: $(3+\sqrt{25})^2$

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Introduction

In mathematics, simplifying expressions is a crucial skill that helps us solve problems efficiently. One of the most common expressions we encounter is the square of a binomial, which can be simplified using the formula $(a+b)^2 = a^2 + 2ab + b^2$. In this article, we will simplify the expression $(3+\sqrt{25})^2$ using this formula.

Understanding the Expression

The given expression is $(3+\sqrt{25})^2$. To simplify this expression, we need to understand the concept of square roots and binomial expansion. 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 $4 \times 4 = 16$. In this expression, we have $\sqrt{25}$, which is equal to 5, because $5 \times 5 = 25$.

Simplifying the Expression

Now that we have understood the expression, let's simplify it using the formula $(a+b)^2 = a^2 + 2ab + b^2$. In this case, $a = 3$ and $b = \sqrt{25} = 5$. Substituting these values into the formula, we get:

$$(3+\sqrt{25})^2 = 3^2 + 2 \times 3 \times 5 + 5^2$$

Expanding the Expression

Now, let's expand the expression by evaluating the terms:

$$3^2 = 9$$

$$2 \times 3 \times 5 = 30$$

$$5^2 = 25$$

Combining the Terms

Now, let's combine the terms to simplify the expression:

$$(3+\sqrt{25})^2 = 9 + 30 + 25$$

Evaluating the Expression

Finally, let's evaluate the expression by adding the terms:

$$(3+\sqrt{25})^2 = 64$$

Conclusion

In this article, we simplified the expression $(3+\sqrt{25})^2$ using the formula $(a+b)^2 = a^2 + 2ab + b^2$. We started by understanding the concept of square roots and binomial expansion, and then applied the formula to simplify the expression. The final answer is 64.

Frequently Asked Questions

• What is the square root of 25? The square root of 25 is 5.
• How do we simplify the expression $(3+\sqrt{25})^2$? We simplify the expression using the formula $(a+b)^2 = a^2 + 2ab + b^2$.
• What is the final answer to the expression $(3+\sqrt{25})^2$? The final answer is 64.

Further Reading

If you want to learn more about simplifying expressions, you can check out the following resources:

• Khan Academy: Simplifying Expressions
• Mathway: Simplifying Expressions
• Wolfram Alpha: Simplifying Expressions

References

• [1] Khan Academy. (n.d.). Simplifying Expressions. Retrieved from https://www.khanacademy.org/math/algebra/x2f1f4f/simplifying-expressions
• [2] Mathway. (n.d.). Simplifying Expressions. Retrieved from https://www.mathway.com/subjects/simplifying-expressions
• [3] Wolfram Alpha. (n.d.). Simplifying Expressions. Retrieved from https://www.wolframalpha.com/input/?i=simplifying+expressions
  

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Introduction

In our previous article, we simplified the expression $(3+\sqrt{25})^2$ using the formula $(a+b)^2 = a^2 + 2ab + b^2$. In this article, we will answer some frequently asked questions related to simplifying expressions.

Q&A

Q1: What is the square root of 25?

A1: The square root of 25 is 5.

Q2: How do we simplify the expression $(3+\sqrt{25})^2$?

A2: We simplify the expression using the formula $(a+b)^2 = a^2 + 2ab + b^2$.

Q3: What is the final answer to the expression $(3+\sqrt{25})^2$?

A3: The final answer is 64.

Q4: Can we simplify expressions with negative numbers?

A4: Yes, we can simplify expressions with negative numbers using the same formula $(a+b)^2 = a^2 + 2ab + b^2$. However, we need to be careful when multiplying negative numbers.

Q5: How do we simplify expressions with fractions?

A5: We can simplify expressions with fractions by multiplying the numerator and denominator by the same number to eliminate the fraction.

Q6: Can we simplify expressions with variables?

A6: Yes, we can simplify expressions with variables using the same formula $(a+b)^2 = a^2 + 2ab + b^2$. However, we need to be careful when working with variables.

Q7: How do we simplify expressions with exponents?

A7: We can simplify expressions with exponents by using the power rule of exponents, which states that $(a^m)^n = a^{mn}$.

Q8: Can we simplify expressions with radicals?

A8: Yes, we can simplify expressions with radicals by using the formula $\sqrt{a} \times \sqrt{b} = \sqrt{ab}$.

Q9: How do we simplify expressions with absolute values?

A9: We can simplify expressions with absolute values by using the formula $|a| = a$ if $a \geq 0$ and $|a| = -a$ if $a < 0$.

Q10: Can we simplify expressions with trigonometric functions?

A10: Yes, we can simplify expressions with trigonometric functions by using the formulas for the sum and difference of angles.

Conclusion

In this article, we answered some frequently asked questions related to simplifying expressions. We covered topics such as simplifying expressions with negative numbers, fractions, variables, exponents, radicals, absolute values, and trigonometric functions.

Frequently Asked Questions

• What is the square root of 25?
• How do we simplify the expression $(3+\sqrt{25})^2$?
• What is the final answer to the expression $(3+\sqrt{25})^2$?
• Can we simplify expressions with negative numbers?
• How do we simplify expressions with fractions?
• Can we simplify expressions with variables?
• How do we simplify expressions with exponents?
• Can we simplify expressions with radicals?
• How do we simplify expressions with absolute values?
• Can we simplify expressions with trigonometric functions?

Further Reading

If you want to learn more about simplifying expressions, you can check out the following resources:

• Khan Academy: Simplifying Expressions
• Mathway: Simplifying Expressions
• Wolfram Alpha: Simplifying Expressions

References

• [1] Khan Academy. (n.d.). Simplifying Expressions. Retrieved from https://www.khanacademy.org/math/algebra/x2f1f4f/simplifying-expressions
• [2] Mathway. (n.d.). Simplifying Expressions. Retrieved from https://www.mathway.com/subjects/simplifying-expressions
• [3] Wolfram Alpha. (n.d.). Simplifying Expressions. Retrieved from https://www.wolframalpha.com/input/?i=simplifying+expressions