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Question 8 of 10

What are the first two steps in solving the radical equation below?

[tex]\[ \sqrt{x+3} - 7 = 15 \][/tex]

A. Square both sides and then add 7 to both sides.

B. Square both sides and then subtract 3 from both sides.

C. Add 7 to both sides and then subtract 3 from both sides.

D. Add 7 to both sides and then square both sides.

Sagot :

GinnyAnsweridn
To solve the radical equation [tex]\(\sqrt{x+3} - 7 = 15\)[/tex], we follow these steps:

### Step 1: Add 7 to both sides
First, we want to isolate the square root term. To do this, we add 7 to both sides of the equation:
[tex]\[ \sqrt{x+3} - 7 + 7 = 15 + 7 \][/tex]
Simplifying this, we get:
[tex]\[ \sqrt{x+3} = 22 \][/tex]

### Step 2: Square both sides
Next, to eliminate the square root, we square both sides of the equation:
[tex]\[ (\sqrt{x+3})^2 = 22^2 \][/tex]
This simplifies to:
[tex]\[ x + 3 = 484 \][/tex]

So, the first two steps in solving the equation [tex]\(\sqrt{x+3} - 7 = 15\)[/tex] are:
1. Add 7 to both sides of the equation.
2. Square both sides of the equation.

Therefore, the correct option is:
D. Add 7 to both sides and then square both sides.
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