Question

What is the highest power of 2 in the following expression? 1800*25*4 square root 8*21 square root 2* 45 square root -2?

Answer 1

225 is the answer I think so

Answer 2

Answer:

The Highest power of 2 is 6

Solution:

$1800 \times 25 \times 4 \sqrt{8 \times 21 \sqrt{2 \times 45 \sqrt{-2}}}$

We have to breakdown the equation in terms of powers of 2,

1800 can be written as $2^{3} \times 5 \times 5 \times 9$

4 can be written as $2^{2}$

8 as $2^{2} \times 2$

Therefore,  

$2^{3} \times 5 \times 5 \times 9 \times 2^{2} \times 25 \sqrt{2^{2} \times 2 \times 21 \sqrt{2 \times 45 \sqrt{-2}}}$

On taking the $2^{2}$ out of the root we get,

$2^{3} \times 5 \times 5 \times 9 \times 2^{2} \times 25 \times 2^{1} \sqrt{2 \times 21 \sqrt{2 \times 45 \sqrt{-2}}}$

$2^{3+2+1} \times 5 \times 5 \times 9 \times 25 \sqrt{2 \times 21 \sqrt{2 \times 45 \sqrt{-2}}}$

$2^{6} \times 5 \times 5 \times 9 \times 25 \sqrt{2 \times 21 \sqrt{2 \times 45 \sqrt{-2}}}$

So, the highest power of 2 is 6