Final answer:
To solve the quadratic equation (2a^2)^2 = 100 using the square roots property, simplify the equation and isolate the variable a. Then, take the square root of both sides to find the values of a.
Step-by-step explanation:
To solve the quadratic equation (2a^2)^2 = 100 using the square roots property, we can simplify the equation by expanding (2a^2)^2 as 4a^4. So, 4a^4 = 100. To isolate a, we take the square root of both sides of the equation:
√(4a^4) = √100
Which simplifies to:
2a^2 = ±10
Dividing both sides by 2a^2 gives us:
a^2 = ±5
Taking the square root of both sides gives us:
a = ±√5