Question

Which of the following is a rational number?

square root 97square root 98, square root 99, square root 100

square root 97
square root 98
square root 99
square root 100

Part A: Find a rational number that is between 5.2 and 5.5. Explain why it is rational. (2 points)

Part B: Find an irrational number that is between 5.2 and 5.5. Explain why it is irrational. Include the decimal approximation of the irrational number to the nearest hundredth. (3 points)

Answer 1

Square root of 100.

Explanation:

Step-by-step explanation:

We can write 10 as a fraction 10/1, therefore,
`\sqrt{}`100 is a rational number.

Part A : A rational no. between 5.2 and 5.5 is 5.3.

It is rational because it can be expressed in the form

p/q where p and q are integers and q is not equal to 0, which is 53/10

Part B: A rational no. between 5.2 and 5.5 is 5.29150262213

An irrational number between 5.2 and 5.5 is 5.29150262213. It is irrational because there is no pattern that repeats and it cant be written as a fraction of two whole numbers.

Answer 2

Explanation:

Square root of all prime numbers is irrational.

97 is an prime number. So √97 is an irrational number.

√98 =
`√(2*7*7)=7√(2)` is an irrational number.

`√(99)=√(3*3*11) =3√(11)` is an irrational number

√100 = 10 is a rational number.

Part A:

5.3 is a rational number.

Rational can be written in p/q form and when divided the result will either terminating decimal or non terminating repeating decimal

Part B:

5.3020050......

Irrational numbers are non terminating non repeating numbers