When multiplying two square roots, multiply the numbers inside the roots and then solve the problem:
[tex]\sqrt[]{a}\cdot\sqrt[]{b}=\sqrt[]{a\cdot b}[/tex]In this problem:
[tex]\sqrt[]{-180}\cdot\sqrt[]{10}=\sqrt[]{-1800}[/tex]Using the same rule above, you can divide the square root into 1800 and -1:
[tex]\sqrt[]{-1800}=\cdot\sqrt[]{1800}\cdot\sqrt[]{-1}[/tex]Using i = ā-1
[tex]\sqrt[]{1800}\cdot i[/tex]Now, let's factor 1800:
1800 |2
900 |2
450 |2
225 |3
75 |3
25 |5
5 |5
1
So, 1800 = 2*2*2*3*3*5*5
Then,
[tex]\begin{gathered} \sqrt[]{1800}i=\sqrt[]{2\cdot2\cdot2\cdot3\cdot3\cdot5\cdot5}i \\ =2\cdot3\cdot5\cdot\sqrt[]{2}i \\ =30i\sqrt[]{2} \end{gathered}[/tex]Answer: 30iā2.
