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The square root property is a crucial technique for solving quadratic equations of the form \(ax^2 = c\). This method allows us to solve for the variable by taking the square root of both sides of the equation.

The main idea is:

• If \(x^2 = a\), then \(x = \pm \sqrt{a}\).

Now, let's see this in action with our example \(5y^2 = 35\). First, we need to isolate \(y^2\) (covered in the next section), and then take the square root of both sides. This gives us \(y = \pm \sqrt{7}\). Don't forget to consider both the positive and negative roots!

Using the square root property makes solving quadratics more straightforward by reducing the variable square to its base value. Make sure to apply it correctly by remembering to include both possible roots.

Isolating terms is a fundamental step when solving equations. To isolate a term means to get the variable by itself on one side of the equation. This involves manipulating the equation using addition, subtraction, multiplication, and division.

In our example, we start with \(5 y^2 - 35 = 0\). To isolate the quadratic term \(5 y^2\), follow these steps:

• Add 35 to both sides: \(5 y^2 = 35\).
• Divide both sides by 5 to get: \(y^2 = 7\).

By isolating \(y^2\), we simplify the equation, making it easier to apply the square root property in the next step. Always ensure that you correctly isolate the term to maintain the equation's balance.

Solving quadratic equations is a common challenge in algebra. Quadratics take the form \(ax^2 + bx + c = 0\) and can be solved using various methods including factoring, completing the square, and the quadratic formula. However, for simple forms like \(5 y^2 = 35\), using the square root property is efficient.

Our example highlights these steps:

• Isolate the quadratic term: \(5 y^2 = 35\).
• Simplify: \(y^2 = 7\).
• Apply the square root property: \(y = \pm \sqrt{7}\).

With practice, these steps become routine. Remember the critical steps: isolating terms and appropriately applying mathematical properties. This approach helps solve quadratics efficiently and accurately.