Chapter 10 Pythagorean Theorm, Radicals, Distance Formula

Question 1

Simplifying Radicals

Answer 1

1) Find the highest perfect square that divides the square root evenly. Ex. Sqr. of 75= Sqr. of 253
2) Simplify the perfect square. Ex. Sqr. of 253= 5Sqr. of 3
3) Multiply any numbers outside the square root symbol of necessary. Ex. (34)Sqr. of 3=12*Sqr. of 3

Question 2

Multiplying and Dividing radicals Properties

Answer 2

Numbers on the outside multiply/divide by the numbers on the outside and stay on the outside. The numbers on the inside multiply/divide by the numbers on the inside and stay on the inside.

Question 3

Dividing by an irrational number

Answer 3

Ex. of irrational numbers are Sqr. of 5 and the Sqr. of 2.
Process:
3Sqr. of 6/Sqr. of 5Sqr. of 5/Sqr. of 5
3(Sqr. of 56)/(Sqr. of 55)
3Sqr. of 30/Sqr. of 25
3*Sqr. of 30/5

Question 4

The converse of the Pythagorean Theorem

Answer 4

If c^2=a^2+b^2 then the triangle is a right triangle. If greater than, it is obtuse. (Check obtuse answers to make sure they are actually a triangle. The two smaller sides added should be more than the longest side.) Of less than, the triangle is acute. 
Ex. Given lengths: 15-36-39
39^2|?|36^2+15^2
1521|?|1296+225
1521=1521 the triangle is right.

Question 5

Special right triangle: 45-45-90

Answer 5

The hypotenuse is the length of one leg squared.
Ex. The leg is 4in long. The hypotenuse is 4(Sqr. of 2)in long.
The leg is the length of the hypotenuse divided by the square root of 2.
Ex. The hypotenuse is 18in long. The leg is 9(Sqr. of 2)in long.

Question 6

Special right triangle: 30-60-90

Answer 6

The hypotenuse is twice the length of the short leg.
Ex. The short leg is 4in. The hypotenuse is 8in.
The long leg is the length of the short leg times the square root of 3.
Ex. The short leg is 4in. The long leg is 4(Sqr. of 3)in.
The short leg is the hypotenuse divided by two or the long leg divided by the square root of 3.

Question 7

Distance formula

Answer 7

D^2={Sqr. of (x2-x1)^2+(y2-y1)^2}

Question 8

Slope formula

Answer 8

M= {(y2-y1)/2,(x2-x1)/2}

Question 9

Pythagorean theorem formula

Answer 9

c^2=a^2+b^2