Digits, Grade 8, Volume 1, Homework Helper

#### Part 1

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 xy.

• 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

• 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.

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