Respuesta :
Answer:
D. [tex]\sqrt{100}[/tex]
Step-by-step explanation:
We have been given four numbers. We are asked to find the rational number from our given choices.
We know that a number is known as rational number if we can write it as a fraction.
Let us see our given choices one by one.
A. [tex]\sqrt{97}[/tex]
[tex]\sqrt{97}=9.8488578017961047[/tex]
Since [tex]\sqrt{97}[/tex] has non repeating and non terminating decimal, therefore, [tex]\sqrt{97}[/tex] is not a rational number.
B. [tex]\sqrt{98}[/tex]
[tex]\sqrt{98}=9.8994949366116653[/tex]
Since [tex]\sqrt{98}[/tex] has non repeating and non terminating decimal, therefore, [tex]\sqrt{98}[/tex] is not a rational number.
C. [tex]\sqrt{99}[/tex]
[tex]\sqrt{99}=9.9498743710661995[/tex]
Since [tex]\sqrt{99}[/tex] has non repeating and non terminating decimal, therefore, [tex]\sqrt{99}[/tex] is not a rational number.
D. [tex]\sqrt{100}[/tex]
[tex]\sqrt{100}=\sqrt{10^2}=10[/tex]
We can write 10 as a fraction [tex]\frac{10}{1}[/tex], therefore, [tex]\sqrt{100}[/tex] is a rational number.
