express in terms of i: \n\\sqrt{-26} =

Explanation:

Step1: Recall the definition of imaginary unit

The imaginary unit ( i ) is defined as ( i = \sqrt{-1} ), so we can rewrite ( \sqrt{-a} ) (where ( a>0 )) as ( \sqrt{a}\cdot\sqrt{-1} ). For ( \sqrt{-26} ), we can split the square root: ( \sqrt{-26}=\sqrt{26\times(- 1)} )

Step2: Apply the property of square roots

Using the property ( \sqrt{ab}=\sqrt{a}\cdot\sqrt{b} ) (for ( a\geq0,b\geq0 ), and here we extend it to the case where ( b = - 1 ) with the definition of ( i )), we have ( \sqrt{26\times(-1)}=\sqrt{26}\cdot\sqrt{-1} ) Since ( \sqrt{-1}=i ), then ( \sqrt{26}\cdot\sqrt{-1}=\sqrt{26}i )

Answer:

(\sqrt{26}i)