Question

What is the sum of 7√28x^6 + 4√x^6 in simplest form, if x ≠ 0?

A) 11√28x^6
B) 11√32x^6
C) 11√36x^6
D) 11√42x^6

Answer 1

The expression 7√28x^6 + 4√x^6 simplifies to 14x^3√7 + 4x^3. None of the provided answer choices matches this result, which suggests an issue with either the calculation or the answer options.

Step-by-step explanation:

The provided problem requires us to simplify the sum of two radicals with variables. We are given the expression 7√28x^6 + 4√x^6 and we need to determine its simplest form. Let's simplify the expression step by step:

can be simplified because 28 is a product of 4 (which is a perfect square) and 7.

Hence, √28x^6 = √(4⋅7)x^6 = 2x^3√7.

Secondly, we see that √x^6 is also simplifiable since x^6 is a perfect square, therefore √x^6 = x^3.

Now we substitute the simplified radicals back into the original expression:

7(2x^3√7) + 4(x^3) = 14x^3√7 + 4x^3

Since these terms are not like terms (they do not have the same radical part), we cannot combine them. Hence, the answer remains 14x^3√7 + 4x^3.

The answer choices provided (A, B, C, D) do not include our result, which indicates that either there has been a mistake in the calculation, or the provided answer choices are incorrect.