Chapter 9

For the following problems, simplify each of the radical expressions. $$ \sqrt{a^{2}-10 a+25} $$

For the following problems, simplify each expression by removing the radical sign. $$ \sqrt{9 m^{6} n^{4}(m+n)^{18}} $$

Perform the indicated operations: $$ \frac{15 x^{2}-20 x}{6 x^{2}+x-12} \cdot \frac{8 x+12}{x^{2}-2 x-15} \div \frac{5 x^{2}+15 x}{x^{2}-25} $$

The resonance frequency \(f\) in an electronic circuit containing inductance \(L\) and capacitance \(C\) in series is given by \(f=\frac{1}{2 \pi \sqrt{L C}}\) (a) Determine the resonance frequency in an electronic circuit if the inductance is 9 and the capacitance is 0.0001 . Use \(\pi=3.14\). (b) Determine the inductance in an electric circuit if the resonance frequency is 5.308 and the capacitance is 0.0001 . Use \(\pi=3.14\).

Simplify each expression by performing the indicated operation. $$ \frac{6-\sqrt{2}}{4+\sqrt{12}} $$

For the following problems, simplify each of the radical expressions. $$ \sqrt{b^{2}+6 b+9} $$

For the following problems, simplify each expression by removing the radical sign. $$ \sqrt{25 m^{26} n^{42} r^{66} s^{84}} $$

Simplify \(\sqrt{x^{4} y^{2} z^{6}}\) by removing the radical sign.

If two magnetic poles of strength \(m\) and \(m\) units are at a distance \(r\) centimeters \((\mathrm{cm})\) apart, the force \(F\) of repulsion in air between them is given by \(F=\frac{m m}{r^{2}}\) (a) Determine the force of repulsion if two magnetic poles of strengths 22 and 46 units are 8 cm apart. (b) Determine how far apart are two magnetic poles of strengths 14 and 16 units if the force of repulsion in air between them is 42 units.

Simplify each expression by performing the indicated operation. $$ \frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}} $$

For the following problems, simplify each of the radical expressions. $$ \sqrt{\left(a^{2}-2 a+1\right)^{4}} $$

For the following problems, simplify each expression by removing the radical sign. $$ \sqrt{(f-2)^{2}(g+6)^{4}} $$

Simplify \(\sqrt{12 x^{3} y^{5} z^{8}}\)

Simplify each expression by performing the indicated operation. $$ \frac{\sqrt{6 a}-\sqrt{8 a}}{\sqrt{8 a}+\sqrt{6 a}} $$

For the following problems, simplify each of the radical expressions. $$ \sqrt{\left(x^{2}+2 x+1\right)^{12}} $$

Simplify each expression by performing the indicated operation. $$ \frac{\sqrt{2 b}-\sqrt{3 b}}{\sqrt{3 b}+\sqrt{2 b}} $$

Solve the inequality \(3(a+2) \leq 2(3 a+4)\).

For the following problems, simplify each expression by removing the radical sign. $$ -\sqrt{64 r^{4} s^{22}} $$

Simplify \(\left(\frac{x^{5} y^{3}}{x^{2} y}\right)^{5}\)

Graph the inequality \(6 x \leq 5(x+1)-6\).

For the following problems, simplify each expression by removing the radical sign. $$ -\sqrt{121 a^{6}(a-4)^{8}} $$

Simplify \(\left(8 x^{3} y\right)^{2}\left(x^{2} y^{3}\right)^{4}\).

Supply the missing words. When looking at a graph from left-to-right, lines with ___________ slope rise, while lines with ___________ slope fall.

For the following problems, simplify each expression by removing the radical sign. $$ -\left[-\sqrt{(w+6)^{2}}\right] $$

Write \((x-1)^{4}(x-1)^{-7}\) so that only positive exponents appear.

Simplify the complex fraction \(\frac{5+\frac{1}{x}}{5-1}\).

For the following problems, simplify each expression by removing the radical sign. $$ -\left[-\sqrt{4 a^{2} b^{2}\left(c^{2}+8\right)^{2}}\right] $$

Simplify \(\sqrt{27 x^{5} y^{10} z^{3}}\).

Simplify \(\sqrt{121 x^{4} w^{6} z^{8}}\) by removing the radical sign.

For the following problems, simplify each expression by removing the radical sign. $$ \sqrt{1.21 h^{4} k^{4}} $$

Simplify \(\frac{1}{2+\sqrt{x}}\) by rationalizing the denominator.

For the following problems, simplify each expression by removing the radical sign. $$ \sqrt{2.25 m^{6} p^{6}} $$

For the following problems, simplify each expression by removing the radical sign. $$ -\sqrt{\frac{169 a^{2} b^{4} c^{6}}{196 x^{4} y^{6} z^{8}}} $$

For the following problems, simplify each expression by removing the radical sign. $$ -\left[\sqrt{\frac{81 y^{4}(z-1)^{2}}{225 x^{8} z^{4} w^{6}}}\right] $$

Find the quotient. \(\frac{x^{2}-1}{4 x^{2}-1} \div \frac{x-1}{2 x+1}\).

Find the sum. \(\frac{1}{x+1}+\frac{3}{x+1}+\frac{2}{x^{2}-1}\).

Solve the equation, if possible: \(\frac{1}{x-2}=\frac{3}{x^{2}-x-2}-\frac{3}{x+1}\).

Perform the division: \(\frac{15 x^{3}-5 x^{2}+10 x}{5 x}\).

Perform the division: \(\frac{x^{3}-5 x^{2}+13 x-21}{x-3}\).