Simplify the following expression:

[tex]\[ 5 \sqrt{7} + \sqrt{7} - 2 \sqrt{7} \][/tex]

Choose the correct simplified form:

A. [tex]\( 3 \sqrt{7} \)[/tex]

B. [tex]\( 3 \sqrt{21} \)[/tex]

C. [tex]\( 4 \sqrt{21} \)[/tex]

D. [tex]\( 4 \sqrt{7} \)[/tex]



Answer :

Let's solve the expression step-by-step.

The given expression is:

[tex]\[ 5\sqrt{7} + \sqrt{7} - 2\sqrt{7} \][/tex]

Step 1: Identify the like terms.
The terms [tex]\(5\sqrt{7}\)[/tex], [tex]\(\sqrt{7}\)[/tex], and [tex]\(-2\sqrt{7}\)[/tex] have a common factor, [tex]\(\sqrt{7}\)[/tex].

Step 2: Group the coefficients of like terms.
[tex]\[ 5\sqrt{7} + \sqrt{7} - 2\sqrt{7} = (5 + 1 - 2)\sqrt{7} \][/tex]

Step 3: Perform the arithmetic operations on the coefficients.
[tex]\[ 5 + 1 - 2 = 4 \][/tex]

Step 4: Multiply the result by [tex]\(\sqrt{7}\)[/tex].
[tex]\[ 4\sqrt{7} \][/tex]

Hence, the expression [tex]\(5\sqrt{7} + \sqrt{7} - 2\sqrt{7}\)[/tex] simplifies to [tex]\(4\sqrt{7}\)[/tex].

Thus, the correct answer is:

[tex]\[ 4\sqrt{7} \][/tex]