Math

QuestionChoose the irrational number from the options: a. 14\frac{1}{4}, b. 47\sqrt{47}, c. 899\frac{89}{9}, d. 43\frac{4}{3}.

Studdy Solution

STEP 1

Assumptions1. We understand that a rational number can be expressed as a fraction of two integers, where the denominator is not zero. . An irrational number cannot be expressed as a fraction of two integers. It is a number that cannot be written as a simple fraction.
3. The square root of a non-perfect square is an irrational number.

STEP 2

Let's examine each option one by one.
a. 14\frac{1}{4}This is a fraction of two integers, so it is a rational number.

STEP 3

b. 47\sqrt{47}47 is not a perfect square, so the square root of47 is an irrational number.

STEP 4

c. 899\frac{89}{9}This is a fraction of two integers, so it is a rational number.

STEP 5

d. 43\frac{4}{3}This is a fraction of two integers, so it is a rational number.

STEP 6

After examining all the options, we find that 47\sqrt{47} is the only irrational number among the options.
So, the answer is option b. 47\sqrt{47}

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