Instructions

A "Pythagorean Triple" is a set of positive integers, a, b and c that fits the rule: a2+ b2= c2.

Here is a list of a few Pythagorean Triples:

(3, 4, 5)

(5, 12, 13)

(6, 8, 10)

(7, 24, 25)

(8, 15, 17)

(9, 40, 41)

(10, 24, 26)

(11, 60, 61)

(12, 35, 37)

(13, 84, 85)

(14, 48, 50)

(15, 112, 113)

(16, 63, 65)

(17, 144, 145)

(18, 80, 82)

(19, 180, 181)

(20, 21, 29)

(20, 99, 101)

(21, 220, 221)

(23, 264, 265)

Pick a Pythagorean Triple and use the Pythagorean Theorem to verify that

a2+ b2= c2. Explain your step-by-step approach to solving the problem.

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step-by-step explanation:

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: