Question 339116
1) Find:
{{{sqrt(27/16)}}}
{{{sqrt(27) = 3sqrt(3)}}}
{{{sqrt(16) = 4}}} so...
{{{highlight(sqrt(27/16) = 3*sqrt(3)/4))}}}
2) Solve:
{{{3+sqrt(x^2-8x) = 0}}} First, subtract 3 from both sides.
{{{sqrt(x^2-8x) = -3}}} Now square both sides.
{{{x^2-8x = 9}}} Next, subtract 9 from both sides.
{{{x^2-8x-9 = 0}}} Factor this trinomial.
{{{(x+1)(x-9) = 0}}} Now apply the zero product rule.
{{{x+1 = 0}}} or {{{x-9 = 0}}} so...
{{{highlight(x = -1)}}} or {{{highlight(x = 9)}}}
3) Simplify:
{{{(1-sqrt(x))^2}}}
{{{(1-sqrt(x))*(1-sqrt(x)) = highlight(1-2*sqrt(x)+x)}}}