Answer :
To determine which choices are equivalent to the expression [tex]\(5 \sqrt{3}\)[/tex], we need to evaluate each of the given choices and compare them to the original expression.
### Original Expression:
[tex]\[ 5 \sqrt{3} \][/tex]
### Choices:
Choice 1: [tex]\(5 \sqrt{3}\)[/tex]
This is identical to the original expression, so it is equivalent.
Choice 2: [tex]\(\sqrt{15}\)[/tex]
To check if these are equivalent, compare the expressions:
[tex]\[ 5 \sqrt{3} \neq \sqrt{15} \][/tex]
The expression [tex]\(\sqrt{15}\)[/tex] is not equivalent because the values under the square roots are different.
Choice 3: [tex]\(5 \times 1.732\)[/tex]
This is using the approximate decimal value for [tex]\(\sqrt{3} \approx 1.732\)[/tex]:
[tex]\[ 5 \sqrt{3} \approx 5 \times 1.732 \][/tex]
This means they are approximately, but not exactly equivalent.
Choice 4: [tex]\( (5^2) \times 3 \)[/tex]
This equals [tex]\(25 \times 3 = 75\)[/tex]. The original expression doesn't simplify to 75:
[tex]\[ 5 \sqrt{3} \neq 75 \][/tex]
Thus, this choice is not equivalent.
Choice 5: [tex]\( \sqrt{5} \times \sqrt{3} \)[/tex]
[tex]\[ \sqrt{5} \times \sqrt{3} = \sqrt{15} \][/tex]
So,
[tex]\[ \sqrt{5} \times \sqrt{3} \neq 5 \sqrt{3} \][/tex]
Therefore, this choice is not equivalent.
### Conclusion:
The original expression [tex]\(5 \sqrt{3}\)[/tex] is only equivalent to Choice 1: [tex]\(5 \sqrt{3}\)[/tex]. The other expressions do not match the original value precisely.
### Original Expression:
[tex]\[ 5 \sqrt{3} \][/tex]
### Choices:
Choice 1: [tex]\(5 \sqrt{3}\)[/tex]
This is identical to the original expression, so it is equivalent.
Choice 2: [tex]\(\sqrt{15}\)[/tex]
To check if these are equivalent, compare the expressions:
[tex]\[ 5 \sqrt{3} \neq \sqrt{15} \][/tex]
The expression [tex]\(\sqrt{15}\)[/tex] is not equivalent because the values under the square roots are different.
Choice 3: [tex]\(5 \times 1.732\)[/tex]
This is using the approximate decimal value for [tex]\(\sqrt{3} \approx 1.732\)[/tex]:
[tex]\[ 5 \sqrt{3} \approx 5 \times 1.732 \][/tex]
This means they are approximately, but not exactly equivalent.
Choice 4: [tex]\( (5^2) \times 3 \)[/tex]
This equals [tex]\(25 \times 3 = 75\)[/tex]. The original expression doesn't simplify to 75:
[tex]\[ 5 \sqrt{3} \neq 75 \][/tex]
Thus, this choice is not equivalent.
Choice 5: [tex]\( \sqrt{5} \times \sqrt{3} \)[/tex]
[tex]\[ \sqrt{5} \times \sqrt{3} = \sqrt{15} \][/tex]
So,
[tex]\[ \sqrt{5} \times \sqrt{3} \neq 5 \sqrt{3} \][/tex]
Therefore, this choice is not equivalent.
### Conclusion:
The original expression [tex]\(5 \sqrt{3}\)[/tex] is only equivalent to Choice 1: [tex]\(5 \sqrt{3}\)[/tex]. The other expressions do not match the original value precisely.