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When solving quadratic equations, the square root property is a handy tool. This property states that if you have an equation of the form \(x^2 = c\), then \(x\) can be either the positive or negative square root of \(c\).
Here’s how it works:

• Start with the equation \(x^2 = c\).
• Take the square root of both sides and remember to include both the positive and negative roots.
• You will then have \(x = \pm \sqrt{c}\).

Using this property is very straightforward, but don't forget to consider both solutions! For example, in the provided equation \(w^2 = 121\), taking the square root gives \(w = \pm \sqrt{121}\).

When taking the square root of both sides of a quadratic equation, it's crucial to remember that both positive and negative values are possible solutions.
For an equation \(x^2 = c\), the solutions are \(x = \sqrt{c}\) and \(x = -\sqrt{c}\).

Here's why it's important:

- Quadratic equations have two symmetrical solutions that are equidistant from zero, one positive and one negative.
- Neglecting the negative root means you miss half of the possible solutions and thereby, incorrect answers.

For example, in the equation \(w^2 = 121\), the solutions aren't just \(w = 11\). They also include \(w = -11\). Hence, both \(w = 11\) and \(w = -11\) are correct solutions.

Simplifying square roots is an essential skill in solving quadratic equations. Square roots can often be easily reduced to a simpler form.
For example, to simplify \(\sqrt{121}\), recall that 121 is a perfect square since \(11 \times 11 = 121\). Therefore, \(\sqrt{121} = 11\).

Here are some tips for simplifying square roots:

- Look for perfect squares: Numbers like 4, 9, 16, 25, 36, etc., have whole numbers as square roots.
- Factorize the number: Break down the number into its prime factors and group them into pairs.

Practicing with perfect squares makes the process quicker. In our exercise: \(w = \pm \sqrt{121}\) simplifies directly to \(w = \pm 11\) because 121 is a perfect square.