 # 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.

## Presentation on theme: "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."— Presentation transcript:

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.

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

 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.

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

 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?

 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.

 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)

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

5 -12 11

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

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

 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

 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

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

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

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