question\nwrite \\(\\sqrt{-10}\\) in simplest radical form.\nanswer attempt 1 out of 2

Explanation:

Step1: Recall the imaginary unit

The imaginary unit ( i ) is defined as ( i = \sqrt{-1} ). So we can rewrite ( \sqrt{-10} ) by separating the negative sign inside the square root. [ \sqrt{-10} = \sqrt{(-1) \times 10} ]

Step2: Use the property of square roots

Using the property ( \sqrt{ab} = \sqrt{a} \times \sqrt{b} ) (for ( a \geq 0, b \geq 0 ); here we extend it to complex numbers where ( a=-1 ) and ( b = 10 )), we get: [ \sqrt{(-1) \times 10} = \sqrt{-1} \times \sqrt{10} ] Since ( \sqrt{-1}=i ), this simplifies to: [ i\sqrt{10} ]

Answer:

( i\sqrt{10} )