can √(1+4x) be written as √4√1+x?

Answer 1

If √4√1+x mean √ 4 ∙ √ ( 1 + x )

then √ ( 1 + 4 x ) can't be written as √ 4 √ ( 1 + x )

For √4 √ (1 + x ) use the product rule for radicals:

√ a ∙ √ b = √ ( a ∙ b )

√4 √ (1 + x ) = √ [ 4 ∙ ( 1 + x ) ] = √ ( 4 ∙ 1 + 4 ∙ x ) = √ ( 4 + 4 x )

That is not √ ( 1 + 4 x )