Question 271389
First of all, these are expressions not equations. You solve equations. You simplify expressions.<br>
{{{root(3, 625)/root(3, 25)}}}
The simplest way to simplify this is to recognize that 625 can be divided evenly by 25. So we can use the property of radicals, {{{root(a, p)/root(a, q) = root(a, p/q)}}}, to get 625 and 25 into the same fraction:
{{{root(3, 625/25)}}}
Since 625/25 = 25 we get:
{{{root(3, 25)}}}
The only other simplifying to try is to find perfect cube factors of 25. But there are none (except 1 which is pointless to factor out). So this is our simplified expression.<br>
{{{sqrt(3) - 2root(4, 3) + 4sqrt(3) + 5root(4, 3)}}}
The first and third terms are like terms. And the second and fourth terms are like terms so we can add and subtract them. Just like x + 4x = 5x, {{{sqrt(3) + 4sqrt(3) = 5sqrt(3)}}}. And just like -2x + 5x = 3x, {{{-2root(4, 3) + 5root(4, 3) = 3root(4, 3)}}}. So we end up with:
{{{5sqrt(3) + 3root(4, 3)}}}