Question 73009
a)
{{{sqrt(x-1)=3}}} I'm assuming it looks like this
{{{(sqrt(x-1))^2=(3)^2}}}Square both sides, this undoes the square root.
{{{x-1=9}}}Solve for x
{{{x=10}}}
Check:
{{{sqrt(10-1)=3}}}
{{{sqrt(9)=3}}}
{{{3=3}}}Works
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b)
{{{sqrt(x^3)=8}}}
{{{(sqrt(x^3))^2=8^2}}}Square both sides
{{{x^3=64}}}
{{{3*sqrt(x^3)=3*sqrt(64)}}}Take cube root of both sides. Note: {{{3*sqrt(x)}}} is the cube root of x
{{{x=4}}}
Check:
{{{sqrt(4^3)=8}}}
{{{sqrt(64)=8}}}
{{{8=8}}}Works
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c)
{{{3*sqrt(x^2)=4}}}
{{{sqrt(x^2)=4/3}}}Divide by 3
{{{(sqrt(x^2))^2=(4/3)^2}}}Square both sides
{{{x^2=16/9}}}Simplify the right side
{{{x=4/3}}}Take the square root of both sides and solve
Check:
{{{3*sqrt((4/3)^2)=4}}}
{{{3*sqrt(16/9)=4}}}
{{{3*(4/3)=4}}}
{{{4=4}}}Works
Hope that helps.