91Ó°ÊÓ

Classify the number as rational or irrational. $$\sqrt{400}$$

Multiply and simplify. $$(\sqrt{u}-3)(\sqrt{u}-4)$$

Classify the number as rational or irrational. $$-\sqrt{0.64}$$

Classify the number as rational or irrational. $$\sqrt{1.21}$$

Find the conjugate of the expression. Then find the product of the expression and its conjugate. $$\sqrt{u}-\sqrt{2}$$

Use a calculator to approximate the value of the expression, if possible. Round your answer to three decimal places. $$\frac{-3+8 \sqrt{24}}{2}$$

Estimate the square root to one decimal place without using a calculator. Then check your estimate by using a calculator. $$\sqrt{70}$$

Estimate the square root to one decimal place without using a calculator. Then check your estimate by using a calculator. $$\sqrt{130}$$

Rewrite the expression as a single fraction and simplify. $$\frac{2}{\sqrt{5}}-9$$

Astronomy The orbital period of a planet is the time that it takes the planet to travel around the Sun. You can find the orbital period \(P\) (in Earth years) using the formula \(P=\sqrt{d^{3}}\), where \(d\) is the average distance (in astronomical units, abbreviated \(\mathrm{AU}\) ) of the planet from the Sun. (a) Simplify the formula. (b) Saturn's average distance from the Sun is about \(9.54 \mathrm{AU}\). What is Saturn's orbital period? Round your answer to one decimal place. (c) Venus's average distance from the Sun is about \(0.72 \mathrm{AU}\). What is Venus's orbital period? Round your answer to one decimal place.