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Problem 11

Perform the indicated operations. Simplify all answers as completely as possible. Assume that all variables appearing under radical signs are nonnegative. $$\sqrt{3}(\sqrt{5}+\sqrt{6})$$

Problem 32

Simplify each expression as completely as possible. Be sure your answers are in simplest radical form. Assume that all variables appearing under radical signs are nonnegative. $$\sqrt{4 x^{10} y^{7}}$$

Problem 39

Simplify each expression as completely as possible. Be sure your answers are in simplest radical form. Assume that all variables appearing under radical signs are nonnegative. $$\sqrt{\frac{4}{9}}$$

Problem 43

Simplify each expression as completely as possible. Be sure your answers are in simplest radical form. Assume that all variables appearing under radical signs are nonnegative. $$\sqrt{\frac{5}{6}}$$

Problem 43

Evaluate or simplify each expression. (Assume \(x \geq 0 .)\) $$(\sqrt{25-9})^{2}$$

Problem 45

In each of the following, perform the indicated operations and simplify as completely as possible. Assume all variables appearing under radical signs are non negative. $$8 \sqrt{25}-3 \sqrt{21}$$

Problem 48

Use a calculator to find the following square roots. Round off your answers to the nearest hundredth. $$\sqrt{730}$$

Problem 50

Use a calculator to find the following square roots. Round off your answers to the nearest hundredth. $$\sqrt{58.9}$$

Problem 55

Perform the indicated operations. Simplify all answers as completely as possible. Assume that all variables appearing under radical signs are nonnegative. $$\frac{\sqrt{x y^{3}}}{\sqrt{x^{3} y}}$$

Problem 56

Use a calculator to give decimal approximations rounded to one, two, and three places. $$\sqrt{23}$$

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