A number is shown below. 0.56

Which statement about the number is true?

A. The number is rational and equivalent to 99 56

B. The number is rational and equivalent to 100 1

C. The number is irrational and equivalent to 56

D. The number is irrational and cannot be represented as a fraction written with integers.

D

Step-by-step explanation:

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.

Step-by-step explanation:

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(1)[tex]\sqrt{10}, \sqrt{27}, \sqrt{99}[/tex], (2) [tex]\sqrt{14}, \sqrt{24}, \sqrt{34}, \sqrt{44}, \sqrt{54}[/tex], (3) [tex]\sqrt{0.33}[/tex] are irrational numbers.

Explanation:

(1)

A number is called an irrational number if it can not be written as a simple fraction form. For example [tex]\sqrt{2}, \sqrt{3},\sqrt{5},...[/tex].

If a real number is multiplied by an irrational number then the result is an irrational number.

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

[tex]\sqrt{64}=8[/tex]

Since the result of these square roots are a rational number, therefore [tex]\sqrt{49}, \sqrt{64}[/tex] these are rational numbers and [tex]\sqrt{10}, \sqrt{27}, \sqrt{99}[/tex] are irrational numbers.

(2)

[tex]\sqrt{14} =\sqrt{7} \sqrt{2}[/tex]

[tex]\sqrt{24} =2\sqrt{6}[/tex]

[tex]\sqrt{14} =\sqrt{17} \sqrt{2}[/tex]

[tex]\sqrt{44} =2\sqrt{11}[/tex]

[tex]\sqrt{54} =3\sqrt{6}[/tex]

All the number in the option can not be written in the form of simple fraction, so all the options represents the irrational numbers.

(3)

[tex]0.25=\frac{1}{4}[/tex]

[tex]\sqrt{0.25} =0.5=\frac{1}{2}[/tex]

[tex]\sqrt{0.33} =\frac{\sqrt{33}}{10}[/tex]

Therefore, the number [tex]\sqrt{0.33}[/tex] is an irrational number. The numbers [tex]0.5,\sqrt{0.25}[/tex] are rational numbers.

A.

Step-by-step explanation:

Since the number can be expressed by a fraction, it is a ratio, thus a rational number. For every factor of 10 in the denominator, the number shifts to the right (after the decimal points) by one position.

So, to get from 8034 to 0.8034, you have to shift 4 positions, which means dividing by a 1 with 4 zeros (10000).

It's rational number

Step-by-step explanation:

if a number is non stop it is irrational

it a number stops as it stopped here at 1 so it's a rational number

for question one its a

Step-by-step explanation:

14√

24√ - Irrational

34√ - Irrational

44√ - Irrational

54√ - Irrational

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Explanation:

Level 2

Part 1: √250 would be simplified to 5√10, because you need to find two factors that equal 250. 25 multiplied by 10 are two factors that you can utilize. Because 25 is a perfect square, it could be reduced to 5. Because 10 isn't a perfect square, you leave it as a radical.

Part 2: √250 is an irrational number because it's a non-terminating decimal and you cannot convert it into a fraction, so it wouldn't be rational.

Level 3

Part 1: √150x^5 would be simplified to 5x^2√6x. Again, find two factors that equal the product, 150. 25 multiplied by 6 are two factors that are useable. Just like the first question, 25 is a perfect square, so it can be reduced to 5. 6 is not a perfect square, so you would leave as a radical. Now, moving onto x^5. You can factor out x^4, because it's a perfect square. x^4 can become x^2. Move x^2 next to 5 and x would be left in the radical with 6.

Part 2: It's rational because 2√4 is simply just 2 x 2 because √4 is a perfect square. 4+7=11. 11 can be converted into a fraction, so it wouldn't be irrational.

Level 4

Part 1: 13√750x*5 y*8 would be simplified to 65x^2y^4√30x. Find two factors that equal 750, which are 25 and 30. You know the drill, 25 is reduced to 5 and 30 stays as a radical. Multiply 13 and 5 to get 65. Factor out x^4 out of x^5 to get x^2. x^8 is a perfect square that can be reduced to x^4.

Part 2: Two unique expressions are 4√16+3 and 5√8 x 34. √16 is a perfect square, so it can become 4. 4 x 4 is 16 and 16 + 3 = 19. 19 is a rational number. 5√8 is irrational, so right off the bat, you'll know it's an irrational expression.