Radical Equations 1 - SAT Math Practice - Passport to Advanced Math - Algebra

SAT Math practice solution below, in full. This is Part 1.

Solve this radical equation for x:
((x^1/2) + 3)^2 = 49

Step 1: Take the square root of both sides.
sqrt(((x^1/2) + 3)^2) = sqrt(49)

This simplifies to:
abs((x^1/2) + 3) = 7

The absolute value implies there could be 2 solutions:

Case 1: (x^1/2) + 3 = 7

Case 2: (x^1/2) + 3 = -7

Both 7^2 and -7^2 yield 49.

Let's solve for Case 1 only.

Step 3: Subtract 3 from both sides.
(x^1/2) + 3 - 3 = 7 - 3

This simplifies to:
x^1/2 = 4

Step 4: Square both sides
x = 4^2

The result is:
x = 16

Subscribe and watch Part 2 and learn how to solve for Case 2!

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