Question

Which sum will be irrational?

a. 3 + 2
b. Ì19 + 7/2
c. 18/3 + 11/10000
d. _6 + (_3.251)

Which product will be rational?
A.17.12 * 33
B. Ì of 3 * Ì of 9
C.4*pie
D.- Ì of 20 * 15

A whole number is added to a number with two digits after the decimal point. To make sure the answer is reasonable, how many digits should the sum have after the decimal point?
a.none
b.1
c.2
d.infinitely many

which of the following cereals is the best to buy?

A.280z for $4.29
B.32oz for $4.59
C.36oz for $4.79
D.24oz for $3.59
Which statement about the product is true?
5.5 sqrt of 5

A.the product is irrational
B.the product is rational
C.the product is either rational nor rational
D.there is not enough information provided to answer to question

Answer 1

Which statement about the product is true?
5.5 sqrt of 5
A.the product is irrational
B.the product is rational

Which sum will be irrational?
b. √19 + 7/2

Which product will be rational?
A.17.12 * 33

A whole number is added to a number with two digits after the decimal point. To make sure the answer is reasonable, how many digits should the sum have after the decimal point?
a.none

which of the following cereals is the best to buy?

A.280z for $4.29 = $0.15/oz
B.32oz for $4.59 = $0.14/oz
C.36oz for $4.79 = $0.13/oz (Best BUY)
D.24oz for $3.59 = $0.14/oz

Answer 2

1. Remember that an irrational number is a number that can't be expressed as a ratio of tow integers. In addition, its decimal representation goes on forever without repeating. three points at the end of a decimal (...) indicate that the decimal part goes on forever without repeating.

Lets work out each one of our sums to check which one is irrational.

a.
`3+2=5` Since 5 is an integer, and all integers are rational numbers, so the result of the sum is a rational number.

b.
`√(19) +(7)/(2) = 7.858898...` Since
`√(19)` is and irrational number, and the sum of and irrational number and a rational number is always an irrational number, the result of the sum, 7.858898..., is an irrational number.

c.
`(18)/(3) +(11)/(10000) =(60011)/(10000)` Since both numbers are rational numbers, and rational numbers are closed under addition (the result of adding rational numbers is always a rational number), the result of the sum,
`(60011)/(10000)`, is a rational number.

d.
`-6+(-3.251)=9.251` Since the decimal part of the result is not infinite, the result of the sum is a rational number.

We can conclude that the correct answer is b.
`√(19) +(7)/(2)`

2. A rational number is a number that can be represented as a ratio of tow integers; in other words as a fraction. Its decimal representation is either finite or periodical (a repeating or recurring decimal).

Now, let's work out our multiplications

A.
`17.12*33=564.96` The decimal part of the result is finite; therefore it is a rational number.

B.
`√(3) *√(9) =√(3)*3=3√(3) =5.196152...` The decimal part of the result is goes on forever without repeating; therefore it is an irrational number.

C.
`4*\pi =12.56637...` The decimal part of the result is goes on forever without repeating; therefore it is an irrational number.

D.
`-√(20) *15=-15√(20) =-67.08203...` The decimal part of the result is goes on forever without repeating; therefore it is an irrational number.

We can conclude that the correct answer is A.17.12 * 33

3. To make sure the answer is reasonable, it should have two digits after the decimal point.

Let's check this with an example:

Suppose you and your friend have one orange each. Your friend cuts his orange in halves, and then he cuts the halves in fourths, so he ends up with 4 pieces of orange. Each piece is
`(1)/(4)` (one fourth) of the original orange. Now, suppose that your friend gives you one of his fourth pieces of orange, so you now have 1 orange +
`(1)/(4)` of orange that your fiend gave you. Since
`(1)/(4)` is a rational number, it can be represented as a decimal; in fact
`(1)/(4) =0.25`. Get back to our sum, 1 orange +
`(1)/(4)` orange = 1 orange + 0.25 orange = 1.25 orange. If you don't keep the tow decimals digits in the sum, the answer wouldn't be reasonable.

We can conclude that the correct answer is c.2

4. To check which one of the cereals is the best buy, we are going to divided the ounces of cereals by the amount of money to check how much ounces of cereal we can buy with one dollar:

A.
`(28oz)/(4.29dollar) =6.53` ounces per dollar.

B.
`(32oz)/(4.59dollar) =6.97` ounces per dollar.

C.
`(36oz)/(4.79dollar)=7.52` ounces per dollar.

D.
`(24oz)/(3.59dollar) =6.69` ounces per dollar.

Since you can buy more ounces of cereal C for $1, the correct answer is C.36oz for $4.79

5. Notice that you have the multiplication of a rational number
`5` and an irrational number
`5√(5)`. If you multiply an irrational number by a non-zero rational number, the result will always be an irrational number. Since you are multiplying a non zero rational number (5) and an irrational number (
`5√(5)`), the result will be an irrational number.

`5*5√(5) =55.901699...` The result is indeed an irrational number.

We can conclude that the correct answer is A.the product is irrational.