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Which expressions is below equal a rational number? Choose all that apply

Which expressions is below equal a rational number? Choose all that apply-example-1

2 Answers

5 votes

Answer:

A,D,E

Explanation:

Rational number :That number which can be written as
(p)/(q) where q is not equal to zero and p,q are both integers.

We have to find which number is rational number

1.
6\sqrt 3-√(108)


6\sqrt3-√(6* 6* 3)


6\sqrt3-6\sqrt3=0

0 is rational number by define of rational number .

Hence, option A is true.

B.
\pi\sqrt9

We know that
\pi is a irrational number when we multiply a irrational number with rational number then the number becomes irrational number


\pi√(3* 3)


3\pi

Where 3 is rational number and
\piis a irrational number

Hence, the number
3\pi is a irrational number not rational number.

Therefore, option B is not true.

C.
√(49)+\sqrt5


√(7* 7)-\sqrt5


7-\sqrt5

We know that
\sqrt5 is a irrational number

When we add rational number to irrational number then the number becomes irrational number .

So,
7-\sqrt5 is a irrational number.

Hence, option C is not true.

D.
(5\sqrt3)(4\sqrt3)


20(\sqrt3)^2


20* 3

=60

60 is a rational number because can be written as
(p)/(q) form.

Hence, option D is true.

E.
(1)/(3)+(4)/(5)


(5+12)/(15)


(17)/(15)

It is a rational number because it is in the form of
(p)/(q).

Hence, option E is true.

User Karolina
by
8.1k points
1 vote

Answer:


6√(3) -√(108)


(5√(3))(4√(3))


(1)/(3) +(4)/(5)

Explanation:

we know that

A rational number is a number that can be written as a ratio of two integers

so

Verify each case

case A)
6√(3) -√(108)

we know that


√(108)=6√(3)

substitute


6√(3) -√(108)=6√(3)-6√(3)=0

The number 0 is a rational number, because can be written as a ratio of two integers

Example
(0)/(1)=0

therefore

The expression is a rational number

case B)
\pi √(9)


\pi √(9)=3\pi

Is not a rational number, because cannot be written as a ratio of two integers

case C)
√(49)+√(5)


√(49)+√(5)=7+√(5)

Is not a rational number, because cannot be written as a ratio of two integers

case D)
(5√(3))(4√(3))


(5√(3))(4√(3))=20*3=60

The number 60 is a rational number, because can be written as a ratio of two integers

Example
(120)/(2)=60

therefore

The expression is a rational number

case E)
(1)/(3) +(4)/(5)


(1)/(3) +(4)/(5)=(5*1+3*4)/(5*3)=(17)/(15)

The number is a rational number, because can be written as a ratio of two integers

therefore

The expression is a rational number

User Istiaque
by
7.7k points

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