Which of the following is equivalent to the radical expression below when x≥7?

√x-7 * √x+1

A) √x^2-6x+7

B) √x^2-6x-7

C) √x^2+8x+7

D) √x^2+8x-7

The answer

the main rule for a square root calculus is given by √A*√B = √A*B, for all value positive of A and B

so we can extended the given value of the fonction as

√x-7 * √x+1 = √x-7 * √x+1 = √ (x-7) * (x+1)

but the extended form of (x-7) * (x+1) is (x-7) * (x+1) = x² + x - 7x - 7 = x²-6x - 7

therefore, √ (x-7) * (x+1) = √ (x²-6x - 7), the value which is equivalent to the radical expression is B) √x^2-6x-7, when x≥7