For each sum or product, determine whether the result is a rational number or an irrational number. Then choose the appropriate reason for each. Result is Result is Reason Rational Irrational (a) 34 + O O (Choose one) The sum of two rationals is always rational. The sum of a rational and an irrational is always irrational. 12 4 + (b) O The sum of two irrationals is sometimes rational, sometimes irrational. The product of two rationals is always rational. 17 21 The product of a nonzero rational and an irrational is always irrational. The product of two irrationals is sometimes rational, sometimes irrational. (c) √√6 x 23 O (Choose one) O O

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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For each sum or product, determine whether the result is a rational number or an irrational number.
Then choose the appropriate reason for each.
Result is Result is
Reason
Rational
Irrational
(a) 34 +
O
O
(Choose one)
The sum of two rationals is always rational.
12
4
The sum of a rational and an irrational is always irrational.
(b)
+
The sum of two irrationals is sometimes rational, sometimes irrational.
The product of two rationals is always rational.
17 21
The product of a nonzero rational and an irrational is always irrational.
The product of two irrationals is sometimes rational, sometimes irrational.
(Choose one)
(c) √√6 x 23
13
(d)
8 x
(Choose one)
19
O
O
O
O
O
O
Transcribed Image Text:For each sum or product, determine whether the result is a rational number or an irrational number. Then choose the appropriate reason for each. Result is Result is Reason Rational Irrational (a) 34 + O O (Choose one) The sum of two rationals is always rational. 12 4 The sum of a rational and an irrational is always irrational. (b) + The sum of two irrationals is sometimes rational, sometimes irrational. The product of two rationals is always rational. 17 21 The product of a nonzero rational and an irrational is always irrational. The product of two irrationals is sometimes rational, sometimes irrational. (Choose one) (c) √√6 x 23 13 (d) 8 x (Choose one) 19 O O O O O O
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