Square Roots All positive real numbers have two square roots, a positive and negative square root. All positive real numbers have two square roots, a positive.

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Presentation transcript:

Square Roots All positive real numbers have two square roots, a positive and negative square root. All positive real numbers have two square roots, a positive and negative square root. The symbol is read as “plus or minus” and refers to both the positive and negative square root. The symbol is read as “plus or minus” and refers to both the positive and negative square root. Negative real numbers do not have real square roots. So there is no solution. Negative real numbers do not have real square roots. So there is no solution. perfect square The square of an integer is called a perfect square. no solution

Not PERFECT??? The square root of a whole number that is NOT a perfect square is an IRRATIONAL NUMBER. numbers that cannot be written as a quotient (fraction, ratio) of two integers and the decimal neither terminates nor repeats. To find the square root of a number that is not a perfect square estimate or use a calculator to find the square root.

Section 10.4 “Use Square Roots to Solve Quadratic Equations” To use square roots to solve a quadratic equation of the form ax² + bx + c = 0, first isolate x² on one side of the equation to obtain x² = d. To use square roots to solve a quadratic equation of the form ax² + bx + c = 0, first isolate x² on one side of the equation to obtain x² = d. x² = d Solving x² = d by Taking Square Roots - If d > 0, then x² = d has two solutions: - If d = 0, then x² = d has one solution: - If d < 0, then x² = d has no solution: no solution Examples

Try It Out… No solution

Take square roots of a fraction In cases where you need to take the square root of a fraction whose numerator and denominator are perfect squares, the radical can be written as a fraction. In cases where you need to take the square root of a fraction whose numerator and denominator are perfect squares, the radical can be written as a fraction. For example, can be written as. For example, can be written as.

Try It Out…

Solve the quadratic equation. Round your answer to the nearest hundredth.