Question

(25−−√ 9 −−−√64−−√ are these rational

Answer 1

( -2.4, 0, 3.1, 81−−√ )

Answer 2

(−2/3, 7/9, π/2

Answer 3

12−−√, 11−−√, π

Answer 4

Match the number with the correct description.(5 points)

0.424242424...

16−−√

0.789

0.133134135...

101−−−√

Irrational because the decimal is non-terminating, non-repeating

Rational because the decimal repeats

Rational because it is the square root of a perfect square

Rational because the decimal terminates

Irrational because the decimal repeats

Irrational because it is the square root of a non-perfect square

Rational because the decimal does not terminate

Answer 5

Between which pair of rational numbers on a number line does 38−−√ lie?(1 point) Responses
Between 6.3 and 6.5

Between 19 and 19.2

Between 18.9 and 19.1

Between 6.1 and 6.2

Answer 6

Yes, since both √9 and √64 are integers (3 and 8, respectively), √9 and √64 are rational numbers. Thus, (25−−√, √9, and √64 are all rational numbers.

Answer 7

Among the given numbers, -2.4 and 3.1 are irrational because they are decimal numbers that cannot be expressed as fractions. On the other hand, 0 is a rational number since it can be written as 0/1.

As for the square root of 81, it is equal to 9, which is a rational number because it can be expressed as a fraction (9/1). So, the numbers in the given list that are rational are: 0 and the square root of 81.

Answer 8

Among the given numbers, -2/3 and 7/9 are rational numbers because they can be expressed as fractions. -2/3 = -0.666... and 7/9 = 0.777..., both of which have repeating decimal representations, but they can still be written as ratios of integers.

On the other hand, π/2 (pi/2) is an irrational number. It is a non-repeating and non-terminating decimal, and cannot be expressed exactly as a fraction.

Therefore, among the given numbers, -2/3 and 7/9 are rational numbers, while π/2 is an irrational number.

Answer 9

Among the given numbers, 12−−√ and 11−−√ are irrational numbers. They cannot be expressed exactly as fractions or as terminating or repeating decimals.

On the other hand, π (pi) is also an irrational number. It is a non-repeating and non-terminating decimal.

Therefore, all three given numbers, 12−−√, 11−−√, and π, are irrational numbers.

Answer 10

0.424242424... - Rational because the decimal repeats
16−−√ - Rational because it is the square root of a perfect square
0.789 - Rational because the decimal terminates
0.133134135... - Irrational because the decimal is non-terminating, non-repeating
101−−−√ - Irrational because it is the square root of a non-perfect square

Answer 11

To determine the pair of rational numbers between which 38−−√ lies, we can estimate its value to the nearest hundredth.

Using a calculator, we find that √38 is approximately equal to 6.164.
Hence, 38−−√ lies between 6.1 and 6.2.

Therefore, the correct option is: Between 6.1 and 6.2.