What Is The Following Product?${ \sqrt{4} \cdot \sqrt{3} }$A. { 2(\sqrt[5]{9}) $}$B. { \sqrt[6]{12} $}$C. { \sqrt[6]{432} $}$D. { 2(\sqrt[6]{3,888}) $}$

Understanding the Problem

The given problem involves the multiplication of two square roots. To solve this, we need to understand the properties of square roots and how they interact with each other when multiplied.

Properties 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. The square root of a number is denoted by the symbol √.

When we multiply two square roots together, we can combine them into a single square root by multiplying the numbers inside the square roots. This is known as the product rule for square roots.

Product Rule for Square Roots

The product rule for square roots states that:

√a × √b = √(a × b)

This means that when we multiply two square roots together, we can combine them into a single square root by multiplying the numbers inside the square roots.

Applying the Product Rule

Now that we understand the product rule for square roots, let's apply it to the given problem.

The problem states that we need to find the product of √4 and √3. Using the product rule, we can combine these two square roots into a single square root by multiplying the numbers inside the square roots.

√4 × √3 = √(4 × 3)

Evaluating the Product

Now that we have combined the two square roots into a single square root, we can evaluate the product.

√(4 × 3) = √12

Simplifying the Square Root

The square root of 12 can be simplified by finding the largest perfect square that divides 12.

12 = 4 × 3

Since 4 is a perfect square, we can rewrite the square root of 12 as:

√12 = √(4 × 3) = √4 × √3 = 2√3

Comparing the Options

Now that we have evaluated the product, let's compare it to the options provided.

A. 2(√5 9) B. √6 12 C. √6 432 D. 2(√6 3888)

None of the options match the product we evaluated, which is 2√3.

Conclusion

In conclusion, the product of √4 and √3 is 2√3. This is not among the options provided, which means that the correct answer is not listed.

Understanding the Problem

The given problem involves the multiplication of two square roots. To solve this, we need to understand the properties of square roots and how they interact with each other when multiplied.

Properties 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. The square root of a number is denoted by the symbol √.

When we multiply two square roots together, we can combine them into a single square root by multiplying the numbers inside the square roots. This is known as the product rule for square roots.

Product Rule for Square Roots

The product rule for square roots states that:

√a × √b = √(a × b)

This means that when we multiply two square roots together, we can combine them into a single square root by multiplying the numbers inside the square roots.

Applying the Product Rule

Now that we understand the product rule for square roots, let's apply it to the given problem.

The problem states that we need to find the product of √4 and √3. Using the product rule, we can combine these two square roots into a single square root by multiplying the numbers inside the square roots.

√4 × √3 = √(4 × 3)

Evaluating the Product

Now that we have combined the two square roots into a single square root, we can evaluate the product.

√(4 × 3) = √12

Simplifying the Square Root

The square root of 12 can be simplified by finding the largest perfect square that divides 12.

12 = 4 × 3

Since 4 is a perfect square, we can rewrite the square root of 12 as:

√12 = √(4 × 3) = √4 × √3 = 2√3

Comparing the Options

Now that we have evaluated the product, let's compare it to the options provided.

A. 2(√5 9) B. √6 12 C. √6 432 D. 2(√6 3888)

None of the options match the product we evaluated, which is 2√3.

Conclusion

In conclusion, the product of √4 and √3 is 2√3. This is not among the options provided, which means that the correct answer is not listed.

Understanding the Problem

The given problem involves the multiplication of two square roots. To solve this, we need to understand the properties of square roots and how they interact with each other when multiplied.

Properties 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. The square root of a number is denoted by the symbol √.

When we multiply two square roots together, we can combine them into a single square root by multiplying the numbers inside the square roots. This is known as the product rule for square roots.

Product Rule for Square Roots

The product rule for square roots states that:

√a × √b = √(a × b)

This means that when we multiply two square roots together, we can combine them into a single square root by multiplying the numbers inside the square roots.

Applying the Product Rule

Now that we understand the product rule for square roots, let's apply it to the given problem.

The problem states that we need to find the product of √4 and √3. Using the product rule, we can combine these two square roots into a single square root by multiplying the numbers inside the square roots.

√4 × √3 = √(4 × 3)

Evaluating the Product

Now that we have combined the two square roots into a single square root, we can evaluate the product.

√(4 × 3) = √12

Simplifying the Square Root

The square root of 12 can be simplified by finding the largest perfect square that divides 12.

12 = 4 × 3

Since 4 is a perfect square, we can rewrite the square root of 12 as:

√12 = √(4 × 3) = √4 × √3 = 2√3

Comparing the Options

Now that we have evaluated the product, let's compare it to the options provided.

A. 2(√5 9) B. √6 12 C. √6 432 D. 2(√6 3888)

None of the options match the product we evaluated, which is 2√3.

Conclusion

In conclusion, the product of √4 and √3 is 2√3. This is not among the options provided, which means that the correct answer is not listed.

Understanding the Problem

The given problem involves the multiplication of two square roots. To solve this, we need to understand the properties of square roots and how they interact with each other when multiplied.

Properties 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. The square root of a number is denoted by the symbol √.

When we multiply two square roots together, we can combine them into a single square root by multiplying the numbers inside the square roots. This is known as the product rule for square roots.

Product Rule for Square Roots

The product rule for square roots states that:

√a × √b = √(a × b)

This means that when we multiply two square roots together, we can combine them into a single square root by multiplying the numbers inside the square roots.

Applying the Product Rule

Now that we understand the product rule for square roots, let's apply it to the given problem.

The problem states that we need to find the product of √4 and √3. Using the product rule, we can combine these two square roots into a single square root by multiplying the numbers inside the square roots.

√4 × √3 = √(4 × 3)

Evaluating the Product

Now that we have combined the two square roots into a single square root, we can evaluate the product.

√(4 × 3) = √12

Simplifying the Square Root

The square root of 12 can be simplified by finding the largest perfect square that divides 12.

12 = 4 × 3

Since 4 is a perfect square, we can rewrite the square root of 12 as:

√12 = √(4 × 3) = √4 × √3 = 2√3

Comparing the Options

Q&A: Understanding the Problem

Q: What is the product of √4 and √3? A: The product of √4 and √3 is 2√3.

Q: Why is the product 2√3? A: The product is 2√3 because we can combine the two square roots into a single square root by multiplying the numbers inside the square roots. This is known as the product rule for square roots.

Q: What is the product rule for square roots? A: The product rule for square roots states that:

√a × √b = √(a × b)

This means that when we multiply two square roots together, we can combine them into a single square root by multiplying the numbers inside the square roots.

Q: How do we simplify the square root of 12? A: We can simplify the square root of 12 by finding the largest perfect square that divides 12.

12 = 4 × 3

Since 4 is a perfect square, we can rewrite the square root of 12 as:

√12 = √(4 × 3) = √4 × √3 = 2√3

Q: Why is the square root of 12 equal to 2√3? A: The square root of 12 is equal to 2√3 because we can rewrite it as the product of two square roots: √4 and √3. This is a result of the product rule for square roots.

Q: What are the options provided in the problem? A: The options provided in the problem are:

A. 2(√5 9) B. √6 12 C. √6 432 D. 2(√6 3888)

Q: Which option is correct? A: None of the options match the product we evaluated, which is 2√3.

Conclusion

In conclusion, the product of √4 and √3 is 2√3. This is not among the options provided, which means that the correct answer is not listed.

Frequently Asked Questions

Q: What is the product of √a and √b? A: The product of √a and √b is √(a × b).

Q: How do we simplify the square root of a number? A: We can simplify the square root of a number by finding the largest perfect square that divides the number.

Q: What is the product rule for square roots? A: The product rule for square roots states that:

√a × √b = √(a × b)

This means that when we multiply two square roots together, we can combine them into a single square root by multiplying the numbers inside the square roots.

Q: Why is the square root of a number equal to the product of two square roots? A: The square root of a number is equal to the product of two square roots because we can rewrite it as the product of two square roots using the product rule for square roots.

Conclusion

In conclusion, the product of √4 and √3 is 2√3. This is not among the options provided, which means that the correct answer is not listed.

Understanding the Problem

The given problem involves the multiplication of two square roots. To solve this, we need to understand the properties of square roots and how they interact with each other when multiplied.

Properties 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. The square root of a number is denoted by the symbol √.

When we multiply two square roots together, we can combine them into a single square root by multiplying the numbers inside the square roots. This is known as the product rule for square roots.

Product Rule for Square Roots

The product rule for square roots states that:

√a × √b = √(a × b)

This means that when we multiply two square roots together, we can combine them into a single square root by multiplying the numbers inside the square roots.

Applying the Product Rule

Now that we understand the product rule for square roots, let's apply it to the given problem.

The problem states that we need to find the product of √4 and √3. Using the product rule, we can combine these two square roots into a single square root by multiplying the numbers inside the square roots.

√4 × √3 = √(4 × 3)

Evaluating the Product

Now that we have combined the two square roots into a single square root, we can evaluate the product.

√(4 × 3) = √12

Simplifying the Square Root

The square root of 12 can be simplified by finding the largest perfect square that divides 12.

12 = 4 × 3

Since 4 is a perfect square, we can rewrite the square root of 12 as:

√12 = √(4 × 3) = √4 × √3 = 2√3

Comparing the Options

Now that we have evaluated the product, let's compare it to the options provided.

A. 2(√5 9) B. √6 12 C. √6 432 D. 2(√6 3888)

None of the options match the product we evaluated, which is 2√3.

Conclusion

In conclusion, the product of √4 and √3 is 2√3. This is not among the options provided, which means that the correct answer is not listed.