5.4 Radical functions practice 1 – equations

Solve the radical equation [math]\sqrt[3]{3x^2+4x+1}-x=1[/math]. If you have two or more answers, write the smallest one.

If [math]x=\sqrt{a}[/math] is a solution to the equation [math]x^2=\sqrt{x^4+3x^2+7}-2[/math], what is the value of [math]a[/math]?

Solve the radical equation [math]\sqrt{3\sqrt{x+1}}=\sqrt{x+3}[/math]. If you have two or more answers, write the smallest one.

Solve the equation [math]\displaystyle{x\sqrt[3]{x+1}-2\sqrt[3]{x+1}=0}[/math]. If you have two or more answers, write the biggest one.

Solve the equation [math]\displaystyle{x-\sqrt{4x}-3=0}[/math]. If you have two or more answers, write the biggest one.

Solve the equation [math]\displaystyle{\sqrt{x-1}+\sqrt{x+4}=5}[/math]. If you have two or more answers, write the biggest one.

How many solutions does the equation [math]\sqrt{x^2-3}+1=0[/math] have?