# How do you simplify # 3sqrt(-8) • isqrt2#?

##### 1 Answer

#### Explanation:

Any non-zero number has two square roots, but when we write *principal* square root.

If

If

If

#x < 0# then#sqrt(x) = i sqrt(-x)#

With these definitions of

If

#a, b >= 0# then#sqrt(a)sqrt(b) = sqrt(ab)#

Note carefully that

#1 = sqrt(1) = sqrt(-1 * -1) != sqrt(-1) * sqrt(-1) = i sqrt(1) * i sqrt(1) = i^2 = -1#

With this in mind, we exercise some care to write:

#3sqrt(-8)*isqrt(2)#

#=3isqrt(8)*isqrt(2)#

#=3i^2 sqrt(8*2)#

#= -3sqrt(16)#

#=-3*4=-12#