Respuesta :
Answer:
The square root of 36/16, that is 1,5
Step-by-step explanation:
First let's see square root of 16/6!
[tex]\sqrt{\frac{16}{6} }[/tex]
the top part of the radical is 4 and the bottom part is square root of 6! that is not a rational number because rational number can be written as the quotient of two whole numbers!
[tex]\sqrt{\frac{16}{6} }=\frac{\sqrt{16} }{\sqrt{6} } =\frac{4}{\sqrt{6}}[/tex]
Then let's take a look at the square root of 36/6,
[tex]\sqrt{\frac{36}{6} } =\frac{\sqrt{36} }{\sqrt{6} } =\frac{6}{\sqrt{6} }[/tex]
due to the fact that it has a root that is not written as a whole number in the denominator, then it is not a rational number!
Now square root of 6
[tex]\sqrt{6}[/tex]
Certainly this square root can be calculated and is equal to 2,449489... but because it has infinite digits after the comma, it can't be written as a quotient!
Finally, the square root of 36/16
[tex]\sqrt{\frac{36}{16} } =\frac{\sqrt{36} }{\sqrt{16} } =\frac{6}{4}=\frac{3}{2} =1,5[/tex]
the square root of 36/16 can be written as a quotient, as it is shown!
Actually it is equal to 1,5, that is the quotient of two whole number: 3/2!
So the square root of 36/16 is our answer!
The rational number among the given options is -the square root of 36/16, that is [tex]\sqrt{\frac{36}{16} }[/tex]
We will start by defining what is meant by a rational number and an irrational number
- A rational number is a number that is of the form p/q where p and q are integers and q is not equal to 0.
- Irrational numbers are the set of real numbers that cannot be expressed in the form of a fraction, p/q where p and q are integers and q is not equal to 0. For example, Non-terminating and non-repeating decimals
Now, to determine which of the options is a rational number, we will examine the options one after the other.
- For the first option - The square root of 16/6
That is,
[tex]\sqrt{\frac{16}{6} }[/tex]
When evaluated, we get
[tex]\sqrt{\frac{16}{6} } = 1.632993161855452...[/tex]
This is a non-repeating and non-terminating decimal, and it cannot be expressed in the form of a fraction, p/q where p and q are integers.
∴ [tex]\sqrt{\frac{16}{6} }[/tex] is not a rational number
- For the second option - the square root of 36/6
That is,
[tex]\sqrt{\frac{36}{6} }[/tex]
When evaluated, we get
[tex]\sqrt{\frac{36}{6} } = 2.449489742783178...[/tex]
This is a non-repeating and non-terminating decimal, and it cannot be expressed in the form of a fraction, p/q where p and q are integers.
∴ [tex]\sqrt{\frac{36}{6} }[/tex] is not a rational number
- For the third option - the square root of 36/16
That is,
[tex]\sqrt{\frac{36}{16} }[/tex]
When evaluated, we get
[tex]\sqrt{\frac{36}{16} } = 1.5[/tex]
This is a terminating decimal and can be expressed in the form of a fraction, p/q where p and q are integers.
The fraction form is [tex](\frac{3}{2} )[/tex]; 3 and 2 are integers
∴ [tex]\sqrt{\frac{36}{16} }[/tex] is a rational number
- For the fourth option - the square root of 6
That is,
[tex]\sqrt{6}[/tex]
When evaluated,
[tex]\sqrt{6} = 2.449489742783178...[/tex]
This is a non-repeating and non-terminating decimal, and it cannot be expressed in the form of a fraction, p/q where p and q are integers.
∴[tex]\sqrt{6}[/tex] is not a rational number.
Hence, the rational number among the given options is -the square root of 36/16, that is [tex]\sqrt{\frac{36}{16} }[/tex]
Learn more here: https://brainly.com/question/24777975
