Mathematics, 29.01.2020 10:58 leahpartaka03

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

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Answer from: lalllda

$6\sqrt{3} -\sqrt{108}$

$(5\sqrt{3})(4\sqrt{3})$

$\frac{1}{3} +\frac{4}{5}$

Step-by-step explanation:

we know that

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

Verify each case

case A) $6\sqrt{3} -\sqrt{108}$

we know that

$\sqrt{108}=6\sqrt{3}$

substitute

$6\sqrt{3} -\sqrt{108}=6\sqrt{3}-6\sqrt{3}=0$

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

Example $\frac{0}{1}=0$

therefore

The expression is a rational number

case B) $\pi \sqrt{9}$

$\pi \sqrt{9}=3\pi$

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

case C) $\sqrt{49}+\sqrt{5}$

$\sqrt{49}+\sqrt{5}=7+\sqrt{5}$

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

case D) $(5\sqrt{3})(4\sqrt{3})$

$(5\sqrt{3})(4\sqrt{3})=20*3=60$

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

Example $\frac{120}{2}=60$

therefore

The expression is a rational number

case E) $\frac{1}{3} +\frac{4}{5}$

$\frac{1}{3} +\frac{4}{5}=\frac{5*1+3*4}{5*3}=\frac{17}{15}$

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

therefore

The expression is a rational number

Answer from: 2022rickskyye

A,D,E

Step-by-step explanation:

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

We have to find which number is rational number

1. $6\sqrt 3-\sqrt{108}$

$6\sqrt3-\sqrt{6\times 6\times 3}$

$6\sqrt3-6\sqrt3=0$

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

$\pi\sqrt{3\times 3}$

$3\pi$

Where 3 is rational number and $\pi$ is a irrational number

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

Therefore, option B is not true.

C. $\sqrt{49}+\sqrt5$

$\sqrt{7\times 7}-\sqrt5$

$7-\sqrt5$

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. $(5\sqrt3)(4\sqrt3)$

$20(\sqrt3)^2$

$20\times 3$

=60

60 is a rational number because can be written as $\frac{p}{q}$ form.

Hence, option D is true.

E. $\frac{1}{3}+\frac{4}{5}$

$\frac{5+12}{15}$

$\frac{17}{15}$

It is a rational number because it is in the form of $\frac{p}{q}$ .

Hence, option E is true.

Answer from: Quest

Now this is something bill nye the science guy should ’s still on disney right?

Answer from: Quest

Jim has run 5/6 of a mile so far. i hope that answers your question! good luck : )

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