Question

Use the square roots property to solve the quadratic equation (2a^2)^2 = 100. If there are multiple answers, list them separated by a comma, e.g. 1,2. If there is no solution, enter ∅.

Answer 1

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