Presentation on theme: "or –5 The side length of a square is the square root of its area."— Presentation transcript:
1 or –5 The side length of a square is the square root of its area. This relationship is shown by a radical symbol Thenumber or expression under the radical symbol is calledthe radicand. The radical symbol indicates only thepositive square root of a number, called the principalroot. To indicate both the positive and negative squareroots of a number, use the plus or minus sign (±).or –5Numbers such as 25 that have integer square roots arecalled perfect squares. Square roots of integers that are notperfect squares are irrational numbers. You can estimatethe value of these square roots by comparing them withperfect squares. For example, lies between and ,so it lies between 2 and 3.
2 5 < Ex 1: Estimate to the nearest tenth. < < 6 5.12 = 26.01 Find the two perfect squares that 27 lies between.<5 << 6Find the two integers that lies betweenBecause 27 is closer to 25 than to 36, is close to 5 than to 6.Try 5.2: = 27.04Too high, try 184.108.40.206 = 26.01Too lowBecause 27 is closer to than 26.01, is closer to 5.2 than to 5.1.Check On a calculator ≈ ≈ 5.1 rounded to the nearest tenth.
3 Notice that these properties can be used to combine quantities under the radical symbol or separate them for the purpose of simplifying square-root expressions. A square-root expression is in simplest form when the radicand has no perfect-square factors (except 1) and there are no radicals in the denominator.
4 Simplify each expression. B.Find a perfect square factor of 32.Product Property of Square RootsProduct Property of Square RootsD.C.Quotient Property of Square RootsQuotient Property of Square Roots
5 If a fraction has a denominator that is a square root, you can simplify it by rationalizing the denominator. To do this,multiply both the numerator and denominator by a numberthat produces a perfect square under the radical sign in thedenominator.Ex 3:Simplify by rationalizing the denominator.A.B.Multiply by a form of 1.Multiply by a form of 1.= 2
6 Square roots that have the same radicand are called like radical terms. To add or subtract square roots, first simplify each radical term and then combine like radical terms by adding or subtracting their coefficients.Ex 4: Adding and Subtracting Square RootsB.A.Simplify radical terms.Combine like radical terms.