Between which two integers does each irrational number lie? A)√6

B)√28
C)√12
D)3√18
E)4√58
F)-3√40

Hey, try

I will do D

3 sqrt 18

= 3 sqrt (9*2)

= 3 sqrt (3*3*2)

= 3*3 sqrt 2

= 9 sqrt 2

= 9 (1.414) around 12.5 or so
which is between 12 and 13

NOW
check that with your calculator (Google calculator if you do not have one on your desk)
3 sqrt(18) = 12.728

To determine between which two integers an irrational number lies, we need to determine the two consecutive integers that the number falls between.

Let's go through each option:

A) √6:
To find the two consecutive integers, we need to calculate the square root of 6, which is approximately 2.45. The two consecutive integers between which √6 lies are 2 and 3. Therefore, the answer is between 2 and 3.

B) √28:
Calculating the square root of 28 gives us approximately 5.29. The two consecutive integers between which √28 lies are 5 and 6. Therefore, the answer is between 5 and 6.

C) √12:
Calculating the square root of 12 gives us approximately 3.46. The two consecutive integers between which √12 lies are 3 and 4. Therefore, the answer is between 3 and 4.

D) 3√18:
Calculating the cube root of 18 gives us approximately 2.62. Multiplying this by 3, we get approximately 7.85. The two consecutive integers between which 3√18 lies are 7 and 8. Therefore, the answer is between 7 and 8.

E) 4√58:
Calculating the fourth root of 58 gives us approximately 2.55. Multiplying this by 4, we get approximately 10.2. The two consecutive integers between which 4√58 lies are 10 and 11. Therefore, the answer is between 10 and 11.

F) -3√40:
Calculating the cube root of 40 gives us approximately 3. <br> Multiplying this by -3, we get -9. The two consecutive integers between which -3√40 lies are -10 and -9. Therefore, the answer is between -10 and -9.

In summary:

A) √6: Between 2 and 3
B) √28: Between 5 and 6
C) √12: Between 3 and 4
D) 3√18: Between 7 and 8
E) 4√58: Between 10 and 11
F) -3√40: Between -10 and -9