Square Roots & Pythagorean Theorem

The opposite of + is - The opposite of is The opposite of x 2 is Inverse Operations…

Square Root of a Number: If b 2 = a, then b is a square root of a

Radical Symbol : Radicand: number inside the radical

All positive numbers have two square roots. POSITIVE OR NEGATIVE Positive square root of a Negative square root of a

Perfect Squares: KNOW 1-20 and their square roots. Perfect Squares: 1,4,9,16,25,36,49,64,81,100,121, 144,169,196,225,256,289,324, 361,400

Irrational Numbers: can’t be written as a fraction

In algebra and geometry, we usually leave answers in radical terms. OR Pull out perfect squares, leave what's left inside the radical

Estimate numbers that aren’t perfect squares. is between 25 and 36 so it’s square root is between 5 and 6. A good estimate would be about 5.5 because 5.5 squared is 30.25

Better estimation: Look for the perfect square on each side of the number. Find the difference from the given number and the smaller number. **This is your numerator.** Find the difference between the larger number and the smaller number.**This is your denominator.**

30 – 25 = 5 36 – 25 = 11 Fraction: 5 / 11 So the square root of 30 is about 5 5 / 11. In a calculator, the answer comes to about So we were very close.

Evaluate : 2 When a=1, b=-2, c=-3 2

Evaluate: OR At 1.12 At

PYTHAGOREAN THEOREM Works only with right triangles a 2 + b 2 = c 2 hypotenuse leg A b C aB c

Find the missing side using Pythagorean Theorem. 8 6 C a 2 + b 2 = c = c = c = c 2 10 = c

12 13 X Find the missing side using Pythagorean Theorem. a 2 + b 2 = c 2 a = 13 2 a = 169 a 2 = 25 a = 5

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