Math

QuestionWhich set has no irrational numbers? {5.15,π,30}\{-5.15, \pi, 30\}, {92,100,5.123}\left\{\frac{9}{2}, \sqrt{100}, 5.123\right\}, or {80,100,6.56}\{\sqrt{80}, 100, 6.56\}?

Studdy Solution

STEP 1

Assumptions1. An irrational number cannot be expressed as a ratio of two integers. . The square root of a non-perfect square is an irrational number.
3. The number π\pi is an irrational number.

STEP 2

We need to identify if any of the numbers in each set are irrational. Let's start with the first set {5.15,π,30}\{-5.15, \pi,30\}.

STEP 3

In the first set, π\pi is an irrational number. So, this set contains an irrational number.

STEP 4

Now, let's move on to the second set {92,100,.123}\left\{\frac{9}{2}, \sqrt{100},.123\right\}.

STEP 5

In the second set, 92\frac{9}{2} is a rational number, 100\sqrt{100} is the square root of a perfect square (which is10, a rational number), and 5.1235.123 is a decimal number which can be expressed as a fraction, hence it's a rational number. So, this set does not contain any irrational numbers.

STEP 6

Finally, let's check the third set {80,100,6.56}\{\sqrt{80},100,6.56\}.

STEP 7

In the third set, 80\sqrt{80} is the square root of a non-perfect square, which makes it an irrational number. So, this set contains an irrational number.
The set that does not contain any irrational numbers is {92,100,5.123}\left\{\frac{9}{2}, \sqrt{100},5.123\right\}.

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