Answer :
To find which choice is equivalent to the expression [tex]\(-\sqrt{27}\)[/tex], we can follow these steps:
1. Simplify [tex]\(\sqrt{27}\)[/tex]:
- Recognize that 27 can be broken down into a product of 9 and 3: [tex]\(27 = 9 \times 3\)[/tex].
- Since 9 is a perfect square, we can simplify [tex]\(\sqrt{27}\)[/tex] as follows:
[tex]\[
\sqrt{27} = \sqrt{9 \times 3} = \sqrt{9} \times \sqrt{3} = 3\sqrt{3}
\][/tex]
2. Apply the negative sign:
- The expression [tex]\(-\sqrt{27}\)[/tex] becomes:
[tex]\[
-\sqrt{27} = - (3\sqrt{3}) = -3\sqrt{3}
\][/tex]
3. Find the equivalent choice:
- The simplified expression is [tex]\(-3\sqrt{3}\)[/tex].
- Looking at the options given, this matches choice E: [tex]\(-3 \sqrt{3}\)[/tex].
Thus, the correct equivalent expression is found in option [tex]\(E\)[/tex].
1. Simplify [tex]\(\sqrt{27}\)[/tex]:
- Recognize that 27 can be broken down into a product of 9 and 3: [tex]\(27 = 9 \times 3\)[/tex].
- Since 9 is a perfect square, we can simplify [tex]\(\sqrt{27}\)[/tex] as follows:
[tex]\[
\sqrt{27} = \sqrt{9 \times 3} = \sqrt{9} \times \sqrt{3} = 3\sqrt{3}
\][/tex]
2. Apply the negative sign:
- The expression [tex]\(-\sqrt{27}\)[/tex] becomes:
[tex]\[
-\sqrt{27} = - (3\sqrt{3}) = -3\sqrt{3}
\][/tex]
3. Find the equivalent choice:
- The simplified expression is [tex]\(-3\sqrt{3}\)[/tex].
- Looking at the options given, this matches choice E: [tex]\(-3 \sqrt{3}\)[/tex].
Thus, the correct equivalent expression is found in option [tex]\(E\)[/tex].