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Published byBartholomew Anderson Modified over 5 years ago

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What does it mean when we see numbers written like this: 4²10² 9² Since our exponent is 2, it means that we multiply the number by itself! So we have 4 x 4, 10 x 10, and 9 x 9.

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When we have a number whose exponent is 2 we use the term “squared”. So, when we see 5², we sometimes say “five squared”.

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Square root : If, then m is the square root of n. Radical sign: represents the positive square root. represents the negative square root. Perfect square: Any number that has an integer square roots. ◦ Examples: 1=1 2, 4=2 2, 9=3 2, 16=4 2, and so on. ◦ This means that the perfect squares in the example above are 1, 4, 9, 16, and so on.

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These are perfect squares. They have the same length and the same width. Area = length ∙ width

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What are the square roots of 81? ◦ 9 2 =81 and (-9) 2 =81. ◦ The square roots of 81 are 9 and -9. ◦ We can write it as ±9. What are the square roots of 49?

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Sometimes, when you find the square roots of a number, the square roots will NOT be WHOLE NUMBERS. This is why you NEED your calculator. Use the square root button to find the square roots. If you get a decimal number, round to the nearest hundredth.

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What are the square roots of 78? What are the square roots of 173? 8.83 and -8.83 (±8.83) 13.15 and -13.15 (±13.15)

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Radical sign: ◦ represents the positive square root. ◦ represents the negative square root.

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5 -12 11

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If you see a problem that looks like this: x²=25 How would you solve it?

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Undo addition and subtraction first. Undo multiplication and division second. Undo squares last.

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Solve the equation. a. x 2 = 25 x 2 = 25 Write original equation. Undo the square. Evaluate square root. When solving for a variable, you will have two answers-the positive and negative square root. x 2 = 25 x = + 5

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Solve the equation. b. h 2 + 5 = 54 Simplify. Undo the square. Evaluate square root. h 2 + 5 = 54 Write original equation. Undo the addition of 5. - 5 -5 h 2 = 49 h = + 7

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Solve the equation. 1. 2. x 2 = 1 x 2 = 81 x = ±1 x = ±9

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3.4. x 2 – 5 = – 112x 2 = 108 x = ±3x = ±2

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