High School

Apex: Which choice is equivalent to the expression below? 2√7 + 8√7
A. 10√14
B. 10√7
C. 16√7
D. 16√14

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:

  1. 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.

  2. Add the coefficients: The coefficients of [tex]\sqrt{7}[/tex] are 2 and 8.

  3. Calculate the sum of the coefficients: [tex]2 + 8 = 10[/tex].

  4. 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}.