3 The side length of a square is the square root of its area The side length of a square is the square root of its area. This relationship is shown by a radical symbol The number or expression under the radical symbol is called the radicand. The radical symbol indicates only the positive square root of a number, called the principal root. To indicate both the positive and negative square roots of a number, use the plus or minus sign (±).or –5
4 Example 1: Estimating Square Roots Estimate to the nearest tenth.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 126.96.36.199 = 26.01Too lowBecause 27 is closer to than 26.01, is closer to 5.2 than to 5.1.Check On a calculator ≈ ≈ 5.2 rounded to the nearest tenth.
5 Estimate to the nearest tenth. Check It Out! Example 1Estimate to the nearest tenth.Find the two perfect squares that –55 lies between.<–7 << –8Find the two integers that lies between –Because –55 is closer to –49 than to –64, is closer to –7 than to –8.Try 7.2: 7.22 = 51.84Too low, try 7.47.42 = 54.76Too low but very closeBecause 55 is closer to than 51.84, is closer to 7.4 than to 7.2.Check On a calculator ≈ – ≈ –7.4 rounded to the nearest tenth.
6 Numbers such as 25 that have integer square roots are called perfect squares. Square roots of integers that are not perfect squares are irrational numbers. You can estimate the value of these square roots by comparing them with perfect squares. For example, lies between and , so it lies between 2 and 3.
7 Square roots have special properties that help you simplify, multiply, and divide them.