What is the first step to take to solve the radical equation 12+x4−10−−−−−−√=8?(1 point)

Responses

Raise both sides of the equation to the second power.
Raise both sides of the equation to the second power.

Subtract 12 from both sides of the equation.
Subtract 12 from both sides of the equation.

Add 10 to both sides of the equation.
Add 10 to both sides of the equation.

Add 12 to both sides of the equation.

1 answer

To solve the radical equation \( \sqrt{12 + x^4 - 10} = 8 \), the first step would be to isolate the radical.

  1. We can simplify the radical first: \( \sqrt{12 + x^4 - 10} \) simplifies to \( \sqrt{x^4 + 2} \).

The equation now looks like this:

\[ \sqrt{x^4 + 2} = 8 \]

Next, raise both sides to the second power to eliminate the square root:

\[ x^4 + 2 = 64 \]

Since the option indicated raising both sides to the second power is the first step to eliminating the radical, the correct response here is:

Raise both sides of the equation to the second power.