How do you simplify 2 square root -49?

2 Answers
Jan 12, 2017

You cannot simplify this question as there is no real number which represents #sqrt(-49)#.

Jan 13, 2017

Answer:

#2 sqrt {- 49} = 14 i#

Explanation:

If we use real numbers, this problem has no solution since there is no real number that is squared #- 49# and therefore, there is no square root of #- 49# in #RR#.

But if we expand the set of numbers we use and use complex numbers #CC#, we have that the imaginary number #i# is:

#i = sqrt {- 1}#.

Taking this definition of number #i# into account we can see that:

#2 sqrt {- 49} = 2 sqrt {49 cdot (- 1)} = 2 sqrt 49 cdot sqrt {- 1} = 2 cdot 7 cdot i = 14 i#