Solve the equation by the square root property. If possible, simplify radicals or rationalize denominators. Express imaginary solutions in the form a+bi.

[X+ 2/3]^2=10/9

take the square root of each side.

Rty

To solve the equation [X + 2/3]^2 = 10/9 using the square root property, follow these steps:

Step 1: Take the square root of both sides of the equation to isolate the squared term.
√[(X + 2/3)^2] = √(10/9)

Step 2: Simplify the radicals on both sides.
X + 2/3 = ±√(10/9)

Step 3: Move the constant term to the other side of the equation.
X = ±√(10/9) - 2/3

Step 4: Simplify the radical and the fraction.
X = ±√10/√9 - 2/3

Step 5: Further simplify the expression.
X = ±√10/3 - 2/3

So, the solutions to the equation are:
X = √10/3 - 2/3
X = -√10/3 - 2/3

Please note that the solutions are expressed in simplified form.

To solve the equation by the square root property, follow these steps:

1. Start with the equation: [X + 2/3]^2 = 10/9

2. Take the square root of both sides of the equation to isolate the squared term. Remember that when you take the square root of a squared term, you get both the positive and negative square roots.

√([X + 2/3]^2) = ± √(10/9)

3. Simplify both sides of the equation:

X + 2/3 = ± √(10/9)

4. Next, isolate the X variable by subtracting 2/3 from both sides of the equation:

X = -2/3 ± √(10/9)

5. Now, let's simplify the radical expression. The square root of 10/9 can be simplified as follows:

√(10/9) = √(10) / √(9) = √(10) / 3

6. Substitute the simplified radical back into the equation:

X = -2/3 ± √(10) / 3

This is the final solution. The equation has two solutions: X = -2/3 + √(10) / 3 and X = -2/3 - √(10) / 3. These are the real solutions.

Since the equation was solved using the square root property, there are no imaginary solutions in this case.