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What is the following sum?

[tex]\[4 \sqrt{5} + 2 \sqrt{5}\][/tex]

A. [tex]\(6 \sqrt{10}\)[/tex]
B. [tex]\(8 \sqrt{10}\)[/tex]
C. [tex]\(6 \sqrt{5}\)[/tex]
D. [tex]\(8 \sqrt{5}\)[/tex]


Sagot :

Let's break down each step to solve the given sum: [tex]\( 4 \sqrt{5} + 2 \sqrt{5} \)[/tex].

1. Identify like terms: In this expression, [tex]\( 4 \sqrt{5} \)[/tex] and [tex]\( 2 \sqrt{5} \)[/tex] are like terms because they both contain the same radical part [tex]\( \sqrt{5} \)[/tex].

2. Add the coefficients: To add like terms, we simply need to add their coefficients. The coefficients of [tex]\( 4 \sqrt{5} \)[/tex] and [tex]\( 2 \sqrt{5} \)[/tex] are 4 and 2, respectively.

[tex]\[ 4 \sqrt{5} + 2 \sqrt{5} = (4 + 2) \sqrt{5} \][/tex]

3. Simplify the expression: Now, we add the coefficients together:

[tex]\[ 4 + 2 = 6 \][/tex]

Therefore, we get:

[tex]\[ (4 + 2) \sqrt{5} = 6 \sqrt{5} \][/tex]

We get that the solution simplifies to [tex]\( 6 \sqrt{5} \)[/tex], which equals approximately 13.416407864998739.

Based on this calculation, the correct answer from the given options is:

[tex]\[ 6 \sqrt{5} \][/tex]