Digits, Grade 8, Volume 1, Homework Helper

1-6: Additional Problem Solving

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

Answers may vary. Sample answers:

  • a. Let x = 3 and y = 4.

    Radical (x2 + y2) = radical (32 + 42): First evaluate exponents, then add the terms.

    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.

    Radical (x + y)2 = radical (3 + 4)2: First evaluate the expression inside the parentheses.

    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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Table of Contents

Digits, Grade 8, Volume 1, Homework Helper Unit A: Number and Operations Unit B: Proportionality Unit C: Expressions, Equations, and Relationships English/Spanish Glossary Formulas Math Symbols Formulas Measures Properties