Question

√1008 simplify

Answer 1

1008 is a funny number, so let's see if we can pull out any perfect squares that can be easily square-rooted.

1008 is 4 x 252. 4 is a perfect square, so:

\[\sqrt{1008}=\sqrt{4 \times 252}=2\sqrt{252}\]
Now we have 252 under the square root sign. Let's keep going. 252 = 4 x 63. 4 is a perfect square, so:

\[2\sqrt{252}=2\sqrt{4 \times 63}=2 \times 2 \sqrt{63}=4 \sqrt{63}\]
Alright, we're getting there, but not done yet! 63 = 9 x 7, and 9 is a perfect square, so:

\[4\sqrt{63}=4\sqrt{9 \times 7}=4 \times 3\sqrt{7}=12\sqrt{7}\]
And that's it! 7 is a prime number, so it can't be factored any further. 12√7 is the simplest form of √1008. Let me know if that made sense, and if you have any questions please ask!