Question

simplify the number using the imaginary unit i √-75

Answer 1

$\sqrt{ - 75} = \sqrt{ - 1 \times 75} = \sqrt{ {i}^{2} \times 75 } = 5i \sqrt{3} \\(therefore \: {i}^{2} = - 1)$

Answer 2

Answer:

$\large\boxed{\sqrt{-75}=5\sqrt3\ i}$

Step-by-step explanation:

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