Question 312691
I need to simplifly radical expressions(no calculator)
1. {{{2sqrt(75) + sqrt(108)}}}
Factor inside the radicals to reveal perfect squares
{{{2*sqrt(25*3) + sqrt(36*3)}}}
Extract the squares
{{{5*2sqrt(3) + 6*sqrt(3)}}}
{{{10*sqrt(3) + 6*sqrt(3)}}}
these are like terms so we just add them
{{{16*sqrt(3)}}}
:
2. {{{sqrt(6)( sqrt(3)+5sqrt(2) )}}}
multiply what's inside the brackets
{{{sqrt(6*3)+5sqrt(6*2)}}}
{{{sqrt(18)+5sqrt(12)}}}
Factor to reveal perfect squares
{{{sqrt(9*2)+5sqrt(4*3)}}}
Extract those squares
{{{3*sqrt(2)+2*5sqrt(3)}}}
{{{3*sqrt(2)+10*sqrt(3)}}}
:
3. {{{(3-sqrt(2))*(3+sqrt(2))}}}
FOIL
{{{9 + 3sqrt(2) - 3sqrt(2) - 2}}}
Middle terms cancel
9 - 2 = 7
:
4. {{{(3sqrt(2))/(5+ sqrt(3))}}}
multiply by the conjugate of the denominator over itself
:{{{(3sqrt(2))/(5+ sqrt(3))}}} * {{{(5-sqrt(3))/(5- sqrt(3))}}} = {{{(15sqrt(2)-3sqrt(3*2))/(25-3)}}} = {{{(15sqrt(2)-3sqrt(6))/(22)}}}
:
5.{{{sqrt(5x+1)+2=6 }}}
subtract 2 from both sides
{{{sqrt(5x+1)=4 }}}
Square both sides
5x + 1 = 16
5x = 16 - 1
5x = 15
x = 3
:
You can check solution in the original equation