Example Finding Examples of Rational and Irrational Numbers
Find values for x and y to make each statement true, if possible. Assume that x and y are natural numbers less than 11 and x ≠ y.
a. square root of x squared , plus , y squared end root is rational.
b. square root of x squared , plus , y squared end root is irrational.
c. square root of open x plus y close squared end root is rational.
d. square root of open x plus y close squared end root is irrational.
Solution
Answers may vary. Sample answers:
a. Let x = 3 and y = 4.
5 is a rational number.
b. Let x = 1 and y = 2.
table with 3 rows and 2 columns , row1 column 1 , square root of x squared , plus , y squared end root , column 2 equals . square root of 1 squared , plus , 2 squared end root , row2 column 1 , , column 2 equals , square root of 1 plus 4 end root , row3 column 1 , , column 2 equals square root of 5 , end table
square root of 5 is a rational number.
c. Let x = 1 and y = 2.
3 is a rational number.
d. Not possible. No matter what the values of x and y, the square of the sum will always be a perfect square. So the square root of that perfect square will always be rational.