Solving Quadratics by Square Roots

The square root of a number x is a value y such that y² = x. For example, the square root of 9 is 3, since 3² = 9.

To solve a quadratic equation of the form $$x^2 = a$$ , take the square root of both sides: $$x = \text{±}\sqrt{a}$$ .

$$n = \text{±}5$$ .

$$n = \text{±}1$$ .

$$m = \text{±}5$$ .

$$t = \text{±}3$$ .

$$4\text{√}2$$ .

To simplify a square root means to express it in its simplest form, removing any perfect square factors.

A perfect square is an integer that is the square of another integer. For example, 1, 4, 9, and 16 are perfect squares.

If $$a = b$$ , then $$a^2 = b^2$$ . This principle is used to solve equations involving square roots.