PRECALCULUS:GRAPHICAL,...-NASTA ED.
PRECALCULUS:GRAPHICAL,...-NASTA ED.
10th Edition
ISBN: 9780134672090
Author: Demana
Publisher: PEARSON
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Chapter P.1, Problem 76E
Solution

a.

Whether the sum is rational number or not when two rational numbers are added.

Yes, because the sum of rational number is, pq+rs=ps+qrps rational as well.

Given:

Two rational numbers are added.

Concept Used:

  • A rational number can be expressed as pq , where p and q are some integers and q≠0 .
  • Sum of integers results in an integer as well.
  • The product of integers is an integer as well.
  • Product of power property: am⋅an=am+n
  • Quotient of powers property: aman=am−n

Calculation:

Let pq, and rs be two rational numbers.

The sum of the rational numbers can be obtained by taking least common denominator (LCD) of both fractions and simplify the numerators over common denominator as shown below

  pq+rs=pq⋅ss+rs⋅qq=psqs+qrqs=ps+qrqs

It implies that the sum of two rational numbers is also a rational number.

b.

Whether the product is rational number or not when two rational numbers are multiplied.

Yes, because the product of rational number is, pq×rs=prps rational as well.

Given:

Two rational numbers are multiplied.

Concept Used:

  • A rational number can be expressed as pq , where p and q are some integers and q≠0 .
  • Sum of integers results in an integer as well.
  • The product of integers is an integer as well.
  • Product of power property: am⋅an=am+n
  • Quotient of powers property: aman=am−n

Calculation:

Let pq, and rs be two rational numbers.

The product of the rational numbers can be obtained by multiplying the numerators and denominators together as shown below

  pq×rs=p×rq×s=prqs

It implies that the product of two rational numbers is also a rational number.

c.

Whether the sum is rational number or not when a rational and an irrational number are added.

No, the sum is always an irrational number.

Given:

A rational and an irrational number are added.

Concept Used:

  • A rational number can be expressed as pq , where p and q are some integers and q≠0 .
  • Sum of integers results in an integer as well.
  • The product of integers is an integer as well.
  • Product of power property: am⋅an=am+n
  • Quotient of powers property: aman=am−n

Calculation:

Since the irrational number added to any number will produce an irrational number, the sum of a rational number and an irrational number is always an irrational number.

d.

Whether the product is rational number or not when a rational and an irrational number are multiplied.

No, the sum is always an irrational number.

Given:

A rational and an irrational number are multiplied.

Concept Used:

  • A rational number can be expressed as pq , where p and q are some integers and q≠0 .
  • Sum of integers results in an integer as well.
  • The product of integers is an integer as well.
  • Product of power property: am⋅an=am+n
  • Quotient of powers property: aman=am−n

Calculation:

Since the irrational number multiplied to any number will produce an irrational number, the product of a rational number and an irrational number is always an irrational number.

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Chapter P.1, Problem 75E
Next
Chapter P.2, Problem 1QR

Chapter P Solutions

PRECALCULUS:GRAPHICAL,...-NASTA ED.

Ch. P.1 - Prob. 1QRCh. P.1 - Prob. 2QRCh. P.1 - Prob. 3QRCh. P.1 - Prob. 4QRCh. P.1 - Prob. 5QRCh. P.1 - Prob. 6QRCh. P.1 - Prob. 7QRCh. P.1 - Prob. 8QRCh. P.1 - Prob. 9QRCh. P.1 - Prob. 10QR
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P.1 - In Exercises 4752, simplify the expression. Assume...Ch. P.1 - Prob. 50ECh. P.1 - Prob. 51ECh. P.1 - Prob. 52ECh. P.1 - Prob. 53ECh. P.1 - Prob. 54ECh. P.1 - Prob. 55ECh. P.1 - Prob. 56ECh. P.1 - Prob. 57ECh. P.1 - Prob. 58ECh. P.1 - Prob. 59ECh. P.1 - Prob. 60ECh. P.1 - Prob. 61ECh. P.1 - Prob. 62ECh. P.1 - Prob. 63ECh. P.1 - In Exercises 63 and 64, use scientific notation to...Ch. P.1 - Prob. 65ECh. P.1 - Prob. 66ECh. P.1 - Prob. 67ECh. P.1 - Prob. 68ECh. P.1 - Prob. 69ECh. P.1 - Prob. 70ECh. P.1 - Prob. 71ECh. P.1 - Prob. 72ECh. P.1 - Prob. 73ECh. P.1 - Prob. 74ECh. P.1 - Prob. 75ECh. P.1 - Prob. 76ECh. P.2 - Prob. 1QRCh. P.2 - Prob. 2QRCh. P.2 - Prob. 3QRCh. P.2 - Prob. 4QRCh. P.2 - Prob. 5QRCh. P.2 - Prob. 6QRCh. P.2 - Prob. 7QRCh. P.2 - Prob. 8QRCh. P.2 - Prob. 9QRCh. P.2 - Prob. 10QRCh. P.2 - Prob. 1ECh. P.2 - Prob. 2ECh. P.2 - Prob. 3ECh. P.2 - Prob. 4ECh. P.2 - Prob. 5ECh. P.2 - Prob. 6ECh. P.2 - Prob. 7ECh. P.2 - Prob. 8ECh. P.2 - Prob. 9ECh. P.2 - Prob. 10ECh. 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