Mathematics, 29.01.2020 10:58 leahpartaka03

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

Answers: 3

Show answers

Answers

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

find out the value of b

step-by-step explanation:

Given matrix a below, and that a=b, find the value of the elements in b

Answer from: Quest

38.5

step-by-step explanation:

lets say, first number = r

second number = 3r+7

total = 49

(r)+(3r+7)= 49

4r+7 = 49

4r = 42

r = 42/4

r= 10.5

3r+7 = 3(10.5)+7 = 38.5

hope this

Another question on Mathematics

Mathematics, 21.06.2019 16:30

If your annual gross income is $62,000 and you have one monthly car payment of $335 and a monthly student loan payment of $225, what is the maximum house payment you can afford. consider a standard 28% front-end ratio and a 36% back-end ratio. also, to complete your calculation, the annual property tax will be $3,600 and the annual homeowner's premium will be $360.

Answers: 1

Answer

Mathematics, 21.06.2019 19:30

The cone in the diagram has the same height and base area as the prism. what is the ratio of the volume of the cone to the volume of the prism? h hl base area-b base area =b volume of cone_1 volume of prism 2 volume of cone 1 volume of prism 3 volume of cone 2 volume of prism 3 oc. od. volume of cone volume of prism e. volume of cone volume of prism 3 2

Answers: 3

Answer

Mathematics, 21.06.2019 23:00

What makes a trapezoid an isosceles trapezoid?

Answers: 2

Answer

Mathematics, 22.06.2019 02:30

In july, the average temperature in one us city was 29°c. by december, the average temperature had fallen by 29°c. explain why the average temperature in december was 0°c.

Answers: 3

Answer

You know the right answer?

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

Questions

Mathematics, 25.09.2019 08:50

Which table represents a linear function...