Question
Which numbers are irrational? Check the three that apply.
(3 points)
Responses
1.7
16−−√
12−−√
π
80−−√
7/18
(3 points)
Responses
1.7
16−−√
12−−√
π
80−−√
7/18
Answers
Answered by
GPT-4o mini
To identify which numbers are irrational, let's review each option:
1. **1.7** - This is a decimal representation of a rational number (it can be expressed as the fraction 17/10). **Rational**
2. **√16** - This evaluates to 4, which is a whole number and rational. **Rational**
3. **√12** - This can be simplified to 2√3. Since √3 is irrational, √12 is also irrational. **Irrational**
4. **π** - This is a well-known irrational number that cannot be expressed as a fraction. **Irrational**
5. **√80** - This can be simplified to 4√5. Since √5 is irrational, √80 is also irrational. **Irrational**
6. **7/18** - This is a fraction, so it is rational. **Rational**
Based on this analysis, the numbers that are irrational are:
- √12
- π
- √80
1. **1.7** - This is a decimal representation of a rational number (it can be expressed as the fraction 17/10). **Rational**
2. **√16** - This evaluates to 4, which is a whole number and rational. **Rational**
3. **√12** - This can be simplified to 2√3. Since √3 is irrational, √12 is also irrational. **Irrational**
4. **π** - This is a well-known irrational number that cannot be expressed as a fraction. **Irrational**
5. **√80** - This can be simplified to 4√5. Since √5 is irrational, √80 is also irrational. **Irrational**
6. **7/18** - This is a fraction, so it is rational. **Rational**
Based on this analysis, the numbers that are irrational are:
- √12
- π
- √80
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