How do you evaluate \sqrt { 3} \cdot \sqrt { - 5}?

1 Answer
Oct 26, 2017

isqrt(15)

Explanation:

One identity you need for this is that

sqrt(a)*sqrt(b)=sqrt(a*b)

So you can factor out the imaginary number sqrt(-1) from the sqrt(-5) to get

sqrt(3)*sqrt(-5) => sqrt(3)*sqrt(5)*sqrt(-1)

Then, we use the identity again to combine the real number parts

sqrt(3)*sqrt(5)*sqrt(-1) => sqrt(3*5)*sqrt(-1)

Finally simplify, and replace sqrt(-1) with i

sqrt(3)*sqrt(-5) => isqrt(15)