91Ó°ÊÓ

Evaluate the expression for the given values of the variables. If it is not possible, state the reason. Round your answers to two decimal places, if necessary. \(\sqrt{5 x-y}\) (a) \(x=3, y=-1\) (b) \(x=-1, y=4\)

Evaluate the expression for the given values of the variables. If it is not possible, state the reason. Round your answers to two decimal places, if necessary. \(\sqrt{x^{2}+3 y}\) (a) \(x=-2, y=-1\) (b) \(x=4, y=0\)

Rationalize the denominator of the expression and simplify. $$\frac{6}{\sqrt{x}-1}$$

Evaluate the expression for the given values of the variables. If it is not possible, state the reason. Round your answers to two decimal places, if necessary. \(\sqrt{z^{2}-4 x}\) (a) \(x=3, z=1\) (b) \(x=-2, z=4\)

Rationalize the denominator of the expression and simplify. (Assume all variables are positive.) $$\sqrt[3]{\frac{1}{8 y^{2}}}$$

Like Terms Are \(2 \sqrt{2}\) and \(3 \sqrt{2}\) like terms? Explain.

Justifying Steps What properties or rules are used to rewrite \(\sqrt{2}(\sqrt{8}-\sqrt{2})\) as \(\sqrt{16}-\sqrt{4}\) in the solution above?

Rationalize the denominator of the expression and simplify. (Assume all variables are positive.) $$\sqrt[3]{\frac{1}{27 a}}$$

Describing a Relationship Describe the relationship between \(\sqrt{2}+1\) and \(\sqrt{2}-1\).

Evaluate the expression for the given values of the variables. If it is not possible, state the reason. Round your answers to two decimal places, if necessary. \(\sqrt{b^{2}-4 a c}\) (a) \(a=4, b=5, c=1\) (b) \(a=-2, b=7, c=3\)