Check my answers please
Is each number rational or irrational
1.-0.6 Rational
2.square root of 40 irrational
3.0.606606660... irrational
4.- square root of 144 rational
5.square root of 12 irrational
6. 0.203040506... irrational
1. - 6/10 right
2. 2 sqrt 10 but sqrt 10 is 3.16227766........ right irrational
3. right
4. -12/1 yes, rational
5. 2 sqrt 3 , sqrt 3 is irrational, right
6. irrational, right
Thank you!
You are welcome.
To check whether a number is rational or irrational, we need to understand the definitions of rational and irrational numbers.
Rational numbers can be expressed as a fraction, where the numerator and denominator are integers. For example, -0.6 can be written as -6/10, which is a ratio of two integers. So, your answer for question 1 is correct, -0.6 is a rational number.
Now, let's move to the second question. The square root of 40 can be simplified as 2√10. Since the square root of 10 is irrational, the square root of 40 is also irrational. Therefore, your answer for question 2 is incorrect, the square root of 40 is irrational.
For question 3, the number 0.606606660... can be written as a repeating decimal, where the digits 606 repeat infinitely. Since repeating decimals can always be expressed as a fraction, 0.606606660... is a rational number. Your answer for question 3 is incorrect, as it is rational.
In question 4, the square root of 144 can be simplified as 12, which is a rational number. Therefore, your answer for question 4 is correct, the square root of 144 is rational.
For question 5, the square root of 12 cannot be simplified into a fraction. It is not a perfect square, so the square root of 12 is indeed an irrational number. Your answer for question 5 is correct, the square root of 12 is irrational.
Lastly, for question 6, the number 0.203040506... seems to have a non-repeating pattern. It does not repeat infinitely, so it is considered an irrational number. Your answer for question 6 is correct, 0.203040506... is irrational.
In summary:
1. Correct: -0.6 is rational.
2. Incorrect: √40 is irrational.
3. Incorrect: 0.606606660... is rational.
4. Correct: -√144 is rational.
5. Correct: √12 is irrational.
6. Correct: 0.203040506... is irrational.