Math

QuestionIdentify the irrational number from the options: a. 98\frac{9}{8}, b. 56\frac{5}{6}, c. 63\sqrt{\frac{6}{3}}, d. 144\sqrt{144}.

Studdy Solution

STEP 1

Assumptions1. An irrational number cannot be expressed as a ratio of two integers. . A rational number can be expressed as a ratio of two integers.
3. The square root of a perfect square is a rational number.
4. The square root of a non-perfect square can be an irrational number.

STEP 2

We will examine each option individually to determine if it is rational or irrational.

STEP 3

Option a is 98\frac{9}{8}, which is a ratio of two integers. Therefore, it is a rational number.

STEP 4

Option b is 6\frac{}{6}, which is a ratio of two integers. Therefore, it is a rational number.

STEP 5

Option c is 3\sqrt{\frac{}{3}}. First, simplify the fraction under the square root.
3=2\sqrt{\frac{}{3}} = \sqrt{2}

STEP 6

2\sqrt{2} is not a perfect square, and its decimal representation is non-terminating and non-repeating. Therefore, it is an irrational number.

STEP 7

Option d is 144\sqrt{144}, which is a perfect square. The square root of a perfect square is a rational number, so 144\sqrt{144} is rational.
The number that is irrational is 2\sqrt{2}.

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