Question

Without simplifying, determine which of the following will represent a rational number. Select all that apply.

A.

423+3√9

B.

423−4√8

C.

423×3√9

D.

423÷4√8

Answer 1

A is rational (A=432)
B is irrational (B=411.6862...) (non repeating)
C is rational (C=3807)
D is irrational (D=299.1061...)

these are the answers but im not sure how to tell without simplifying for this


√8 will never be rational
√9 is a whole number therefore it will come out rational in these equations

Answer 2

Options A and C are correct

The expressions that represent a rational number are 423+3√9  and 423×3√9

A rational number is a number that can be written as a ratio of two integers.

For example, c = a/b represents a rational number if a and b are integers, and b is not equal to zero

Non-terminating decimals are irrational numbers because they cannot be written as a ratio of two integers.

Since √8 is an irrational number, without necessarily simplifying, it is clear that it will make 423−4√8 and 423-3√8 to be irrational

√9 is a rational number because it gives a result that can be written as a ratio of two integers. Therefore, 423+3√9 and 423×3√9 are rational numbers.

The expressions that represent a rational number are 423+3√9  and 423×3√9

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