Square Roots & Pythagorean

Theorem

The opposite of + is -The opposite of is The opposite of x2 is

Inverse Operations…

Square Root of a Number:

If b2 = 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

a Positive square root of aa 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

2 3

In algebra and geometry, we usually leave answers in

radical terms.

428 22

222 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

30

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• 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

5.477225.• So we were very close.

25 36

Evaluate: acb 42

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

2

124

16

4

)3(14)2(

Evaluate:

4321

4321 OR

4321

At 1.12 At - 0.62

PYTHAGOREAN THEOREM

Works only with right triangles

a2 + b2 = c2

hypotenuse

leg

leg

A

b

C a B

c

Find the missing side using Pythagorean

Theorem.

8

6

C

a2 + b2 = c2

82 + 62 = c2

64 + 36 = c2

100 = c2

10 = c

12

13

X

Find the missing side using Pythagorean Theorem.

a2 + b2 = c2

a2 + 122 = 132

a2 + 144 = 169a2 = 25a = 5

Don’t Do This!!!