Simplify The Expression: 504 2 \frac{\sqrt{504}}{\sqrt{2}} 2 ​ 504 ​ ​

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Introduction

Simplifying mathematical expressions is an essential skill in mathematics, and it requires a deep understanding of various mathematical concepts. In this article, we will focus on simplifying the expression $\frac{\sqrt{504}}{\sqrt{2}}$. This expression involves square roots, and simplifying it requires a step-by-step approach. We will break down the expression into smaller parts, simplify each part, and then combine them to obtain the final simplified expression.

Understanding Square Roots

Before we dive into simplifying the expression, let's briefly review the concept of square roots. A 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. We can represent square roots using the symbol $\sqrt{}$. For instance, $\sqrt{16}$ represents the square root of 16.

Simplifying the Expression

Now that we have a basic understanding of square roots, let's simplify the expression $\frac{\sqrt{504}}{\sqrt{2}}$. To simplify this expression, we need to simplify the numerator and the denominator separately.

Simplifying the Numerator

The numerator of the expression is $\sqrt{504}$. To simplify this, we need to find the largest perfect square that divides 504. A perfect square is a number that can be expressed as the product of an integer with itself. For example, 16 is a perfect square because it can be expressed as 4 multiplied by 4.

Let's find the largest perfect square that divides 504. We can start by finding the prime factorization of 504. The prime factorization of 504 is:

$504 = 2^3 \times 3^2 \times 7$

Now that we have the prime factorization of 504, we can identify the largest perfect square that divides 504. The largest perfect square that divides 504 is $2^2 \times 3^2$, which equals 36.

We can rewrite the numerator as:

$\sqrt{504} = \sqrt{2^3 \times 3^2 \times 7}$

Using the property of square roots that $\sqrt{a^2} = a$, we can rewrite the numerator as:

$\sqrt{504} = 2 \times 3 \times \sqrt{7}$

Simplifying further, we get:

$\sqrt{504} = 6\sqrt{7}$

Simplifying the Denominator

The denominator of the expression is $\sqrt{2}$. This is already in its simplest form, so we don't need to simplify it further.

Combining the Simplified Numerator and Denominator

Now that we have simplified the numerator and the denominator, we can combine them to obtain the final simplified expression.

$\frac{\sqrt{504}}{\sqrt{2}} = \frac{6\sqrt{7}}{\sqrt{2}}$

To simplify this expression further, we can rationalize the denominator by multiplying both the numerator and the denominator by $\sqrt{2}$. This will eliminate the square root in the denominator.

$\frac{6\sqrt{7}}{\sqrt{2}} = \frac{6\sqrt{7} \times \sqrt{2}}{\sqrt{2} \times \sqrt{2}}$

Simplifying further, we get:

$\frac{6\sqrt{7}}{\sqrt{2}} = \frac{6\sqrt{14}}{2}$

Finally, we can simplify the expression by dividing the numerator and the denominator by 2.

$\frac{6\sqrt{14}}{2} = 3\sqrt{14}$

Conclusion

In this article, we simplified the expression $\frac{\sqrt{504}}{\sqrt{2}}$ by breaking it down into smaller parts, simplifying each part, and then combining them to obtain the final simplified expression. We used various mathematical concepts, including square roots and prime factorization, to simplify the expression. The final simplified expression is $3\sqrt{14}$.

Frequently Asked Questions

• What is the simplified form of $\frac{\sqrt{504}}{\sqrt{2}}$?
• How do you simplify the expression $\frac{\sqrt{504}}{\sqrt{2}}$?
• What is the largest perfect square that divides 504?
• How do you rationalize the denominator of an expression?

Final Answer

The final simplified expression is $3\sqrt{14}$.

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Introduction

In our previous article, we simplified the expression $\frac{\sqrt{504}}{\sqrt{2}}$ by breaking it down into smaller parts, simplifying each part, and then combining them to obtain the final simplified expression. In this article, we will answer some frequently asked questions related to the simplification of the expression.

Q&A

Q1: What is the simplified form of $\frac{\sqrt{504}}{\sqrt{2}}$?

A1: The simplified form of $\frac{\sqrt{504}}{\sqrt{2}}$ is $3\sqrt{14}$.

Q2: How do you simplify the expression $\frac{\sqrt{504}}{\sqrt{2}}$?

A2: To simplify the expression $\frac{\sqrt{504}}{\sqrt{2}}$, we need to simplify the numerator and the denominator separately. We can start by finding the largest perfect square that divides 504. The largest perfect square that divides 504 is $2^2 \times 3^2$, which equals 36. We can rewrite the numerator as $\sqrt{504} = 6\sqrt{7}$. Then, we can simplify the expression by rationalizing the denominator.

Q3: What is the largest perfect square that divides 504?

A3: The largest perfect square that divides 504 is $2^2 \times 3^2$, which equals 36.

Q4: How do you rationalize the denominator of an expression?

A4: To rationalize the denominator of an expression, we need to multiply both the numerator and the denominator by the conjugate of the denominator. In the case of the expression $\frac{6\sqrt{7}}{\sqrt{2}}$, we can rationalize the denominator by multiplying both the numerator and the denominator by $\sqrt{2}$.

Q5: What is the prime factorization of 504?

A5: The prime factorization of 504 is $2^3 \times 3^2 \times 7$.

Q6: How do you simplify the numerator of the expression $\frac{\sqrt{504}}{\sqrt{2}}$?

A6: To simplify the numerator of the expression $\frac{\sqrt{504}}{\sqrt{2}}$, we need to find the largest perfect square that divides 504. The largest perfect square that divides 504 is $2^2 \times 3^2$, which equals 36. We can rewrite the numerator as $\sqrt{504} = 6\sqrt{7}$.

Q7: What is the final simplified expression of $\frac{\sqrt{504}}{\sqrt{2}}$?

A7: The final simplified expression of $\frac{\sqrt{504}}{\sqrt{2}}$ is $3\sqrt{14}$.

Conclusion

In this article, we answered some frequently asked questions related to the simplification of the expression $\frac{\sqrt{504}}{\sqrt{2}}$. We provided detailed explanations and examples to help readers understand the concepts and techniques involved in simplifying the expression.

Frequently Asked Questions

• What is the simplified form of $\frac{\sqrt{504}}{\sqrt{2}}$?
• How do you simplify the expression $\frac{\sqrt{504}}{\sqrt{2}}$?
• What is the largest perfect square that divides 504?
• How do you rationalize the denominator of an expression?
• What is the prime factorization of 504?
• How do you simplify the numerator of the expression $\frac{\sqrt{504}}{\sqrt{2}}$?
• What is the final simplified expression of $\frac{\sqrt{504}}{\sqrt{2}}$?

Final Answer

The final simplified expression of $\frac{\sqrt{504}}{\sqrt{2}}$ is $3\sqrt{14}$.