Question

Find the product of square root of, 3, end square root 3 ​ and 5, square root of, 3, end square root5 3 ​ in simplest form. Also, determine whether the result is rational or irrational and explain your answer. Answer Attempt 1 out of 2 Result: The result is because it be written as the ratio of two integers and its decimal expansion terminate or repeat.

Answer 1

To find the product of \(\sqrt{3}\) and \(5\sqrt{3}\), we start with the expression:

\[ \sqrt{3} \times 5\sqrt{3} \]

We can rearrange this by multiplying the coefficients with each other and then multiplying the square roots:

\[ = 5 \times \sqrt{3} \times \sqrt{3} \]

Since \(\sqrt{3} \times \sqrt{3} = 3\), we can simplify the expression:

\[ = 5 \times 3 = 15 \]

The result is \(15\).

Now, to determine whether \(15\) is rational or irrational:

A rational number is any number that can be expressed as the quotient of two integers (i.e., in the form \(\frac{a}{b}\) where \(a\) and \(b\) are integers and \(b \neq 0\)). Since \(15\) can be expressed as \(\frac{15}{1}\), it is rational.

In summary, the product of \(\sqrt{3}\) and \(5\sqrt{3}\) is \(15\), which is a rational number because it can be written as the ratio of two integers and its decimal expansion terminates (it is \(15.0\)).

Answer 2

The result is rational because it can be written as the ratio of two integers and its decimal expansion does terminate or repeat. correct?

Answer 3

Yes, you are correct! The result, which is \(15\), is indeed rational because it can be expressed as the ratio of two integers, specifically as \(\frac{15}{1}\). Additionally, since \(15\) is a whole number, its decimal expansion terminates (it is \(15.0\)).

So, you can summarize it as:

"The result is rational because it can be written as the ratio of two integers, and its decimal expansion does terminate."

This explanation is accurate!

Answer 4

Find the product of square root of, 3, end square root 3 ​ and 5, square root of, 3, end square root5 3 ​ in simplest form.

Answer 5

To find the product of \(\sqrt{3}\) and \(5\sqrt{3}\), we can proceed as follows:

1. Write the expression: \[ \sqrt{3} \times 5\sqrt{3} \]

2. Use the property of square roots that states \(\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}\): \[ = 5 \times (\sqrt{3} \times \sqrt{3}) = 5 \times \sqrt{3^2} \]

3. Since \(\sqrt{3^2} = 3\): \[ = 5 \times 3 \]

4. Multiply the numbers: \[ = 15 \]

Thus, the product of \(\sqrt{3}\) and \(5\sqrt{3}\) in simplest form is: \[ \boxed{15} \]

Answer 6

withouth the (){}[] please!

Answer 7

Sure! Here’s the calculation without any parentheses or brackets:

To find the product of square root of 3 and 5 square root of 3:

1. Write the expression: √3 × 5√3

2. Use the property of square roots that states √a × √b = √(a × b): = 5 × √3 × √3 = 5 × √(3 × 3)

3. Since √(3 × 3) = 3: = 5 × 3

4. Multiply the numbers: = 15

Thus, the product of square root of 3 and 5 square root of 3 in simplest form is 15.