# Square roots between two integer values?

• July 1st 2009, 06:28 AM
Sailee316
Square roots between two integer values?
The Square root of 50 lies between what two integer values?

The square root of 50 = 7.0710678118654755 so does it lie between 6 and 8 or 7 and 8??

Thanks
• July 1st 2009, 06:54 AM
skeeter
Quote:

Originally Posted by Sailee316
The Square root of 50 lies between what two integer values?

The square root of 50 = 7.0710678118654755 so does it lie between 6 and 8 or 7 and 8??

Thanks

$7^2 = 49$

$(\sqrt{50})^2 = 50
$

$8^2 = 64$
• July 1st 2009, 07:17 AM
Sailee316
I still don't understand. Which two integers does square root of 50 lie between?

Thanks
• July 1st 2009, 07:22 AM
skeeter
Quote:

Originally Posted by Sailee316
I still don't understand. Which two consecutive integers does square root of 50 lie between?

Thanks

7 and 8
• July 1st 2009, 09:54 AM
HallsofIvy
Quote:

Originally Posted by Sailee316
The Square root of 50 lies between what two integer values?

The square root of 50 = 7.0710678118654755 so does it lie between 6 and 8 or 7 and 8??

7 and 8, of course! Why would you even consider "6 and 8"?

By the way, you don't need a calculator to answer this. $7^2= 49$ and $8^2= 64$ and 50 lies between 49 and 64.

Quote:

Thanks
• July 1st 2009, 10:00 AM
Jazzua
Quote:

I still don't understand. Which two consecutive integers does square root of 50 lie between?
why don't you understand?

The question asked the square root of 50 lies between which two integer values.

the square root of 50 is 7.07. so rephrase the question. 7.07 lies between which two integer values.

well it's greater than 7 and lesser than 8.

so it lies between 7 and 8.
• July 2nd 2009, 03:03 AM
Sailee316
ok i think i get it now.

Ö 150 lies between what two integer values?

Is it 12 and 13?? If so how?

Also how did you get 7 ^2 and 8^2 ?

Thanks
• July 2nd 2009, 03:18 AM
yeongil
Quote:

Originally Posted by Sailee316
150 lies between what two integer values?

Is it 12 and 13?? If so how?

Yes, because $\sqrt{150} \approx 12.25$, which is between 12 and 13.

01
• July 2nd 2009, 04:28 AM
CaptainBlack
Quote:

Originally Posted by yeongil
Yes, because $\sqrt{150} \approx 12.25$, which is between 12 and 13.

01

It is also between 10 and 127, there is an unstated assumption that the question means "consecutive integers". Of course the question may have said exactly that, but you did not think it important enough to mention?

CB
• July 10th 2009, 03:48 AM
HallsofIvy
Quote:

Originally Posted by Sailee316
ok i think i get it now.

Ö 150 lies between what two integer values?

Is it 12 and 13?? If so how?

Also how did you get 7 ^2 and 8^2 ?

Thanks

Are you serious? you get $7^2$ and $8^2$ by multiplying! $7^2= (7)(7)= 49$ and $8^2= (8)(8)= 64$

I also know that $12^2= (12)(12)= 144< 150$ and that $13^2= (13)(13)= 169> 150$. Since 150 lies between 144 and 169, its square root lies between 12 and 13.

As Captain Black pointed out, You can pick any integer whose square is less than 150 and any (positive) integer whose square is larger than 150 and say that the square root of 150 lies between them. But because you specifically asked "what two integers", it was clear that you wanted a single answer and the most reasonable interpretation of that is the two integers closest to that square root.