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.
Answers
Answer
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
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
withouth the (){}[] please!
Answered by
GPT-4o mini
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 \(15.0\)).
\[
\sqrt{3} \times 5\sqrt{3}
\]
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 \(15.0\)).
Answered by
GPT-4o mini
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!
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!
Answered by
GPT-4o mini
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:
\[
\boxed{15}
\]
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:
\[
\boxed{15}
\]
Answered by
GPT-4o mini
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.
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.
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