Question

Please help me on this question Algebra 1 question

Answer 1

A rational number is one which can be made by dividing two integers.
a)
`√(25) + √(9) = 5 + 3 = 8` - 8 is rational because you can divide two whole numbers to get 8, for example, 16/2 = 8.

b) pi is irrational, and cannot be made by dividing two whole numbers. So adding pi to pi will still be irrational.

c) same case as b, pi is irrational so if you add two to it, it's still irrational.

d)
`√(7)` is definitely irrational, because we can't write it as the quotient of two whole numbers. So
`√(7) + 6` is still irrational.

e)
`( √(45))/( √(5) )` can be rewritten as :

`(3 √(5) )/( √(5) )`
which is equal to 3. 3 is a rational number because we can divide two numbers and get three, for example, 6/2 = 3

f) This one is sometimes rational, and sometimes irrational. It depends on the values of x and y. For example, if x is
`- \pi` and y is
`\pi` then:

`x + y = (- \pi ) + ( \pi ) = 0`, and zero is rational.
However, if x =
`\pi` and y =
`\pi`, then:

`x+y = \pi + \pi =2 \pi`, which is irrational.