Math

QuestionIs 12\sqrt{12} a rational number? Choose true or false and explain your choice. A. True, it's an integer. B. True, it has repeating digits. C. False, it never ends or repeats. D. True, it's a terminating decimal.

Studdy Solution

STEP 1

Assumptions1. We are asked to determine if 12\sqrt{12} is a rational number. . A rational number is defined as a number that can be expressed as the quotient or fraction p/q of two integers, with the denominator q not equal to zero.
3. The square root of a number is a value that, when multiplied by itself, gives the original number.

STEP 2

First, let's simplify 12\sqrt{12}.
12=4×=4×=2\sqrt{12} = \sqrt{4 \times} = \sqrt{4} \times \sqrt{} =2\sqrt{}

STEP 3

Now, we know that 3\sqrt{3} is an irrational number because it cannot be expressed as a fraction of two integers and its decimal representation never ends or repeats.

STEP 4

Since 12\sqrt{12} is equal to 232\sqrt{3} and 3\sqrt{3} is irrational, we can conclude that 12\sqrt{12} is also irrational.

STEP 5

Therefore, the statement "12\sqrt{12} is a rational number" is false.

STEP 6

Looking at the answer choices, the correct one isC. False, because the decimal representation of 12\sqrt{12} never ends or repeats.
The statement "12\sqrt{12} is a rational number" is false because the decimal representation of 12\sqrt{12} never ends or repeats.

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