Question

Simplify the number using the imaginary unit i √-75

Answer 1

`\large\boxed{√(-75)=5\sqrt3\ i}`

Explanation:

`i=√(-1)\\\\√(-75)=√((25)(3)(-1))\qquad\text{use}\ √(ab)=√(a)\cdot√(b)\\\\=√(25)\cdot\sqrt3\cdot√(-1)=5\cdot\sqrt3\cdot i=5\sqrt3\ i`

Answer 2

`√( - 75) = √( - 1 * 75) = \sqrt{ {i}^(2) * 75 } = 5i √(3) \\(therefore \: {i}^(2) = - 1)`