Answered

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Combine the radicals below:

[tex]\[ -\sqrt{5} - 3 \sqrt{5} \][/tex]

A. [tex]\(-4 \sqrt{10}\)[/tex]

B. [tex]\(-4 \sqrt{5}\)[/tex]

C. [tex]\(-2 \sqrt{10}\)[/tex]

D. [tex]\(-2 \sqrt{5}\)[/tex]

Please select the best answer from the choices provided:

A

B

C

D

Sagot :

GinnyAnswer
Let's combine the radicals given in the expression:

[tex]\[ -\sqrt{5} - 3\sqrt{5} \][/tex]

Step-by-step solution:

1. Identify the common radicals: Both terms have [tex]\(\sqrt{5}\)[/tex] as the radical component.

2. Combine like terms: You can combine these terms by adding or subtracting their coefficients.

[tex]\[ -\sqrt{5} - 3\sqrt{5} \][/tex]

3. Sum the coefficients: Add the coefficients of [tex]\(\sqrt{5}\)[/tex]:

[tex]\[-1 - 3 = -4\][/tex]

4. Combine the coefficients with the common radical:

[tex]\[ -4 \sqrt{5} \][/tex]

So, the expression simplifies to:

[tex]\[ -4 \sqrt{5} \][/tex]

From the given choices, we see that the correct answer is:

B. [tex]\(-4 \sqrt{5}\)[/tex]
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