Which two consecutive whole numbers does [tex]\sqrt{39}[/tex] lie between? Why?

A. 5 and 6 because 39 falls between [tex]5^2=25[/tex] and [tex]6^2=36[/tex].
B. 4 and 6 because 39 falls between [tex]4^2=16[/tex] and [tex]6^2=36[/tex].
C. 6 and 7 because 39 falls between [tex]6^2=36[/tex] and [tex]7^2=49[/tex].
D. 5 and 7 because 39 falls between [tex]5^2=25[/tex] and [tex]7^2=49[/tex].

Question

05-08-2024
Mathematics

Answered

Which two consecutive whole numbers does [tex]\sqrt{39}[/tex] lie between? Why?

A. 5 and 6 because 39 falls between [tex]5^2=25[/tex] and [tex]6^2=36[/tex].
B. 4 and 6 because 39 falls between [tex]4^2=16[/tex] and [tex]6^2=36[/tex].
C. 6 and 7 because 39 falls between [tex]6^2=36[/tex] and [tex]7^2=49[/tex].
D. 5 and 7 because 39 falls between [tex]5^2=25[/tex] and [tex]7^2=49[/tex].

Answer :

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GinnyAnswer GinnyAnswer · Answer 1 · 2024-08-05T20:40:28-04:00

To determine between which two consecutive whole numbers the square root of 39 lies, we follow these steps:

1. Calculate the square root of 39.
The square root of 39 is approximately [tex]$ 6.245 $[/tex].

2. Identify the two consecutive whole numbers between which this value falls.
- The whole number just below 6.245 is 6.
- The whole number just above 6.245 is 7.

3. Verify that 6 and 7 are indeed the correct bounds by calculating their squares:
- [tex]$ 6^2 = 36 $[/tex]
- [tex]$ 7^2 = 49 $[/tex]

4. Confirm that 39 lies between these squares:
- [tex]$ 36 < 39 < 49 $[/tex]

Therefore, the two consecutive whole numbers between which [tex]$ \sqrt{39} $[/tex] lies are 6 and 7. Hence, the correct choice is:

6 and 7 because 39 falls between [tex]$ 6^2=36 $[/tex] and [tex]$ 7^2=49 $[/tex].