5.4 Radical functions (in class)

Find integers [math]a, b, c, d[/math], and [math]e[/math] such that [math]\sqrt[3]{54(xy^2)^5}=3^ax^by^c\sqrt[3]{2x^dy^e}[/math].

Which of the following expressions is equivalent to [math]\sqrt{9x^4-6x^2+1}[/math]?

If [math]\displaystyle{\frac{1}{1+\sqrt{2}+\sqrt{3}}}=\dfrac{a+\sqrt{b}-\sqrt{c}}{4}[/math] where [math]a, b[/math], and [math]c[/math] are positive integers, what is the value of [math]a+b+c[/math]?

Which of the following expressions is equivalent to [math]\sqrt[4]{48x^4y^8z^9}[/math]?

The figure shows the graph of the function [math]f(x)=\sqrt[3]{ax+b}+c[/math]. Find [math]a+b+c[/math].

What are the domain and range of [math]f(x)=\sqrt{x^2-4x+7}[/math]?

Consider a radical function [math]f(x)=\sqrt{-x^2-10x-16}[/math]. If the domain of [math]f(x)[/math] is [math][a,b][/math] and the range of [math]f(x)[/math] is [math][c,d][/math], what is the value of [math]a+b+c+d[/math]?

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

Solve the radical equation [math]x-\sqrt{x+11}=1[/math]. If you have two or more answers, write the smallest one.

Solve the radical equation [math]\sqrt{2x-5}-\sqrt{3x+4}=-2[/math]. If you have two or more answers, write the smallest one.

If [math]\displaystyle{(\sqrt{2022}-\sqrt{2021})^{2021}(\sqrt{2022}+\sqrt{2021})^{2022}}=\sqrt{a}+\sqrt{b}[/math] where [math]a[/math] and [math]b[/math] are integers and [math]a>b[/math], what is the value of [math]a[/math]?

Solve the equation [math]\dfrac{2}{\sqrt{x}+2}+\dfrac{1}{2\sqrt{x}-1}=\dfrac{10}{21}[/math]. If you have two or more answers, write the biggest one.

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

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

How many integer solutions does the inequality [math]\sqrt{x+3}<4[/math] have?

How many integer solutions does the inequality [math]\sqrt{x-3}+1> x-4[/math] have? (Hint: Graphing)