Answer :
To solve the given expression [tex]2\sqrt{7} + 8\sqrt{7}[/tex], we need to combine the like terms. Both terms contain [tex]\sqrt{7}[/tex], which means we can add their coefficients together similar to how we would with variables.
Here's the step-by-step process:
Identify the like terms: Both terms, [tex]2\sqrt{7}[/tex] and [tex]8\sqrt{7}[/tex], have [tex]\sqrt{7}[/tex] as a common factor.
Add the coefficients: The coefficients of [tex]\sqrt{7}[/tex] are 2 and 8.
Calculate the sum of the coefficients: [tex]2 + 8 = 10[/tex].
Multiply the sum by the common factor: [tex]10\sqrt{7}[/tex].
Thus, the expression [tex]2\sqrt{7} + 8\sqrt{7}[/tex] simplifies to [tex]10\sqrt{7}[/tex].
The correct multiple-choice option is B. 10\sqrt{7}.