Respuesta :

calculista

Answer:

[tex]6\sqrt{3} -\sqrt{108}[/tex]

[tex](5\sqrt{3})(4\sqrt{3})[/tex]

[tex]\frac{1}{3} +\frac{4}{5}[/tex]

Step-by-step 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) [tex]6\sqrt{3} -\sqrt{108}[/tex]

we know that

[tex]\sqrt{108}=6\sqrt{3}[/tex]

substitute

[tex]6\sqrt{3} -\sqrt{108}=6\sqrt{3}-6\sqrt{3}=0[/tex]

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

Example [tex]\frac{0}{1}=0[/tex]

therefore

The expression is a rational number

case B) [tex]\pi \sqrt{9}[/tex]

[tex]\pi \sqrt{9}=3\pi[/tex]

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

case C) [tex]\sqrt{49}+\sqrt{5}[/tex]

[tex]\sqrt{49}+\sqrt{5}=7+\sqrt{5}[/tex]

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

case D) [tex](5\sqrt{3})(4\sqrt{3})[/tex]

[tex](5\sqrt{3})(4\sqrt{3})=20*3=60[/tex]

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

Example [tex]\frac{120}{2}=60[/tex]

therefore

The expression is a rational number

case E) [tex]\frac{1}{3} +\frac{4}{5}[/tex]

[tex]\frac{1}{3} +\frac{4}{5}=\frac{5*1+3*4}{5*3}=\frac{17}{15}[/tex]

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

therefore

The expression is a rational number

lublana

Answer:

A,D,E

Step-by-step explanation:

Rational number :That number which can be written as [tex]\frac{p}{q}[/tex] where q is not equal to zero and p,q are both integers.

We have to find which number is rational number

1.[tex]6\sqrt 3-\sqrt{108}[/tex]

[tex]6\sqrt3-\sqrt{6\times 6\times 3}[/tex]

[tex]6\sqrt3-6\sqrt3=0[/tex]

0 is rational number by define of rational number .

Hence, option A is true.

B.[tex]\pi\sqrt9[/tex]

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

[tex]\pi\sqrt{3\times 3}[/tex]

[tex]3\pi[/tex]

Where 3 is rational number and [tex]\pi[/tex]is a irrational number

Hence, the number [tex]3\pi[/tex] is a irrational number not rational number.

Therefore, option B is not true.

C.[tex]\sqrt{49}+\sqrt5[/tex]

[tex]\sqrt{7\times 7}-\sqrt5[/tex]

[tex]7-\sqrt5[/tex]

We know that [tex]\sqrt5[/tex] is a irrational number

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

So, [tex]7-\sqrt5[/tex] is a irrational number.

Hence, option C is not true.

D.[tex](5\sqrt3)(4\sqrt3)[/tex]

[tex]20(\sqrt3)^2[/tex]

[tex]20\times 3[/tex]

=60

60 is a rational number because can be written as [tex]\frac{p}{q}[/tex] form.

Hence, option D is true.

E.[tex]\frac{1}{3}+\frac{4}{5}[/tex]

[tex]\frac{5+12}{15}[/tex]

[tex]\frac{17}{15}[/tex]

It is a rational number because it is in the form of [tex]\frac{p}{q}[/tex].

Hence, option E is true.

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