√6× 0 rational or irrational
π ÷π rational or irrational
10π - 7π irrational or rational
√49 + 1/3 irrational or rational
these two are the chose irrational or rational
I can see that.
I want to see YOUR choices so I can correct them.
You didn't expect me to just give you the answers, did you?
What purpose would that serve in you learning how to do this?
To determine whether a given number is rational or irrational, we need to understand the definitions of these terms:
1. Rational number: A rational number is any number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero.
2. Irrational number: An irrational number is any number that cannot be expressed as a fraction of two integers. Irrational numbers cannot be written as terminating or repeating decimals.
Now, let's analyze each of the expressions you've provided:
1. √6 × 0:
To determine if this expression is rational or irrational, we need to evaluate it. In this case, the product of the square root of 6 multiplied by 0 is zero. Zero is a rational number because it can be expressed as the fraction 0/1. Therefore, the result is a rational number.
2. π ÷ π:
When we divide any non-zero value by itself, the result is always 1. Hence, π ÷ π equals 1. One is a rational number because it can be written as the fraction 1/1. Therefore, the result is a rational number.
3. 10π - 7π:
Here, we have two multiples of π being subtracted. Simplifying this expression gives us 3π. Since π is an irrational number (it cannot be expressed as a fraction), multiplying it by any rational number (in this case, 3) will still result in an irrational number. Therefore, the result is an irrational number.
4. √49 + 1/3:
The square root of 49 is 7, and adding 1/3 to it results in 7 1/3 or 22/3. This value can be expressed as the fraction 22/3, making it a rational number. Therefore, the result is a rational number.
In summary:
- √6 × 0 is rational.
- π ÷ π is rational.
- 10π - 7π is irrational.
- √49 + 1/3 is rational.