how do i simplify the square root of 3 times the square root of 51

√3 *√51  =

√3 *√(3 * 17) =

√3*√3*√17 =

3√17

√3 + √51 

recognize that 51 has some factors

= √3 + √(3 x 17)

= √3 + √3 x √17

= √3 x 1 + √3 x √17

now, taking out the common factor √3,

= √3 (  ......... )

Can you finish by working out what goes inside those brackets?  🍦🍦🃏

BTW, students may contend that the result does not look any simpler than what we started with, but to a mathematician it is. Really!

Taking out a common factor is always considered simplifying an expression.