Algebra: Rational and Irrational Numbers

Determine if sums and products of rational and irrational numbers are rational or irrational, based on the high school Common Core standard #N-RN.3. For #grade9 #grade10 #grade1...

What type of number is √7?

Rational Irrational
If p is a prime number, what type of number is √p?

always rational sometimes rational and sometimes irrational always irrational
If √3 is multiplied by a nonzero rational number, what type of number is the product?

always rational sometimes rational and sometimes irrational always irrational
The sum of a rational and an irrational number is...

always rational sometimes rational and sometimes irrational always irrational
Which number is rational?

5 + π (2/7) + 0.891 √2 + 1 (3/8) + (√5/2)
Which number is rational?

7√2 5π √3/2 (9/10) (2.673)
Which number is irrational?

(1/6)⋅(π/2) √4 + 5 √3⋅√3 √2 − √2
The sum of two rational numbers is...

always rational sometimes rational and sometimes irrational always irrational
Which number is rational?

(1/2) + 7.4 − √2 √2 + √2 √2⋅√18 0π − 31.4
Complete this proof: A is rational, B is irrational and A + B = C. C cannot be rational because

C + A would then be rational, and this equals B. C + A would then be irrational, and this equals B. C – A would then be rational, and this equals B. C – A would then be irrational, and this equals B.
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