2 Simplifying Square Roots An expression written with a radical symbol is called a radical expression, or a radical.The number or expression inside the radical is the radicand.
3 Calculator keystrokes Example 1Use a Calculator to Find Square RootsFind the square root of 52. Round your answer to the nearest tenth. Check that your answer is reasonable.SOLUTIONCalculator keystrokesorDisplayRounded value≈ 7.252This is reasonable, because 52 is between the perfect squares 49 and 64. So, should be between and , or 7 and 8. The answer 7.2 is between 7 and 8.5264493
4 Example 2Find Side LengthsUse the Pythagorean Theorem to find the length of the hypotenuse to the nearest tenth.SOLUTIONa2 + b2 = c2Write Pythagorean Theorem.= c223Substitute for a and for b.2 + 3 = c2Simplify.5 = c2Add.Take the square root of each side.= c5Use a calculator.2.2 ≈ c4
5 Multiply the radicals. Then simplify if possible. Example 3Multiply RadicalsMultiply the radicals. Then simplify if possible.b.28a.37SOLUTIONa.37=b.=28=21=16= 45
6 Simplify the radical expression. Example 4Simplify RadicalsSimplify the radical expression.a.12b.45SOLUTION=a.1243b.4595==43=95= 23= 356
7 Now You Try Evaluate, Multiply, and Simplify RadicalsFind the square root. Round your answer to the nearest tenth. Check that your answer is reasonable.1.27ANSWER5.2; < < , so 5 < 5.2 < 6.2527362.46ANSWER6.8; < < , so 6 < 6.8 < 7.4636493.8ANSWER2.8; < < , so 2 < 2.8 < 3.4894.97ANSWER9.8; < < , so 9 < 9.8 < 10.9781100
8 Multiply the radicals. Then simplify if possible. CheckpointNow You Try Evaluate, Multiply, and Simplify RadicalsMultiply the radicals. Then simplify if possible.5.35ANSWER156.116ANSWER667.273ANSWER98.5315ANSWER
9 Simplify the radical expression. CheckpointNow You Try Evaluate, Multiply, and Simplify RadicalsSimplify the radical expression.9.20ANSWER2510.8ANSWER211.75ANSWER5312.112ANSWER47