Exam 8: Radical Expressions and Equations

Find the length of the third side of the right triangle. Assume that $c$ represents the length of the hypotenuse. Give an exact answer and, if appropriate, an approximation to three decimal places. - $a=5, b=5$

Solve the equation. - $y=\sqrt{3 y+10}$

Solve the equation. - $\sqrt{5 q-4}=\sqrt{5 q+4}$

Identify the radicand. - $\sqrt{\mathrm{x}+5}$

Rationalize the denominator and simplify. - $\sqrt{\frac{36}{5}}$

Multiply and then, if possible, simplify by factoring. - $\sqrt{10} \sqrt{14}$

Use a calculator to approximate the square root. Round to three decimal places. - $\sqrt{1.03}$

Find the length of the third side of the right triangle. Assume that $c$ represents the length of the hypotenuse. Give an exact answer and, if appropriate, an approximation to three decimal places. - $b=20, c=25$

Find the length of the third side of the right triangle. Where appropriate, give both an exact answer and an approximation to three decimal places. -

Add or subtract. Simplify by collecting like radical terms, if possible. - $-6 \sqrt{72}-5 \sqrt{50}+9 \sqrt{200}$

Divide and simplify. - $\frac{\sqrt{16 x}}{\sqrt{4 x}}$

Find the length of the third side of the right triangle. Where appropriate, give both an exact answer and an approximation to three decimal places. -

Solve the equation. - $\sqrt{6 q-5}=5$

Provide an appropriate response. - $\sqrt{4} \cdot \sqrt{9}=\sqrt{4 \cdot 9}$

Solve the equation. - $\mathrm{x}+6=6 \sqrt{\mathrm{x}+1}$

Provide an appropriate response. -Explain the error in the following: $\sqrt{\mathrm{x}^{2}-36}=\sqrt{\mathrm{x}^{2}}-\sqrt{36}=\mathrm{x}-6$ .

Decide whether or not the radical expression represents a real number. - $-\sqrt{-140}$

Perform the indicated operation. - $\sqrt{12} \sqrt{4}-3 \sqrt{75}$

Simplify by factoring. - $\sqrt{150 x^{2} y}$

Multiply and then, if possible, simplify by factoring. - $\sqrt{7} \sqrt{7 x}$