Solve the equation by using the square root property.
Simplify all radicals.
(a) x2 = 256
(b) t 2 = -144
√256 = 16
(a) x^2 = 256
To solve for x using the square root property, we take the square root of both sides of the equation.
√(x^2) = √256
x = ±√256
Simplifying the square root of 256, which is a perfect square, we have:
x = ±16
Therefore, the solutions to the equation x^2 = 256 are x = 16 and x = -16.
(b) t^2 = -144
In this case, we have a squared term equal to a negative value. Since the square of any real number cannot be negative, there are no real solutions to this equation.
Therefore, the equation t^2 = -144 has no real solutions.
To solve the equations using the square root property, we need to isolate the variable on one side of the equation and then take the square root of both sides.
(a) x^2 = 256:
Step 1: Start by isolating the variable on one side of the equation. Since x^2 is equal to 256, we can write it as:
x^2 - 256 = 0
Step 2: Now we can apply the square root property, which states that if a^2 = b, then a = √b or a = -√b. In this case, the square root of 256 is 16, so we have:
x - 16 = 0 or x + 16 = 0
Step 3: Solve for x by adding or subtracting 16 from both sides of the equation:
For x - 16 = 0, adding 16 to both sides gives us: x = 16
For x + 16 = 0, subtracting 16 from both sides gives us: x = -16
So the solutions to the equation x^2 = 256 are x = 16 and x = -16.
(b) t^2 = -144:
Step 1: Start by isolating the variable on one side of the equation. Since t^2 is equal to -144, we can write it as:
t^2 + 144 = 0
Step 2: Applying the square root property, we need to find the square root of -144. However, since the square root of a negative number does not exist in the real number system, this equation has no real solutions.
Therefore, there are no solutions to the equation t^2 = -144.