91Ó°ÊÓ

It is difficult to measure the height of a tall tree, particularly when it is growing in a dense forest. However, it is relatively easy to measure its base diameter. The formula $$h=0.84 d^{\frac{2}{3}}$$ models a tree's height, \(h,\) in meters, in terms of its base diameter, \(d,\) in centimeters. (Source: Thomas McMahon, Scientific American, July, 1975 ) a. The largest known sequoia, the General Sherman in California, has a base diameter of 985 centimeters (about the size of a small house). Use a calculator to approximate the height of the General Sherman to the nearest tenth of a meter. b. Rewrite the formula in radical notation.

In Exercises \(53-74\), rationalize each denominator. Simplify, if possible. $$\frac{16}{\sqrt{11}+3}$$

Multiply as indicated. If possible, simplify any square roots that appear in the product. $$(\sqrt{10}-3)(\sqrt{10}-5)$$

Find the indicated root, or state that the expression is not a real number. $$\sqrt[4]{1}$$

The formula $$A=1.83 w^{\frac{2}{3}}$$ models the area of an egg shell, \(A\), in square centimeters, in terms of its weight, \(w,\) in grams. a. An ostrich egg weighs approximately 1600 grams. Use a calculator to approximate the shell's area to the nearest tenth of a square centimeter. b. Rewrite the formula in radical notation.

In Exercises \(55-68,\) multiply and, if possible, simplify. $$\sqrt{8 x} \cdot \sqrt{10 y}$$

In Exercises \(53-74\), rationalize each denominator. Simplify, if possible. $$\frac{15}{\sqrt{7}+2}$$

Find the indicated root, or state that the expression is not a real number. $$\sqrt[5]{1}$$

Multiply as indicated. If possible, simplify any square roots that appear in the product. $$(\sqrt{10}-4)(\sqrt{10}-6)$$

In Exercises \(55-68,\) multiply and, if possible, simplify. $$\sqrt{12 x} \cdot \sqrt{3 x}$$