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Application of Equations with 
Radicals & Rational Exponents 
Hypotenuse 
c 
a 
b 
Leg 
Leg
• Pythagorean Theorem 
푐 = √푎2 + 푏2 
a= √c²- b² 
b= √c²-a²
Steps in 
solving
Example 
A community billboard 
has sides 5 meters and 12 
meters. What is the 
length of it diagonal?
Step One: 
Illustrate 
12 M 
5 
M 
???
Step Two 
Write the given 
a=5 b=12 c=?
Step 3 
Write the formula 
C = √a² +b²
Step 4 
Substitute 
C= √12²+ 5²
Step 5 
Square the given 
C= √144+ 25
Step 6 
Add or Subtract 
√169
Step 7 
Find the roots 
c= 13

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Application of Equations with Radical and Rational Exponents