Some collectors view comics as an investment the effective

Question

Simplifying Algebraic Expressions Involving Radicals-

1. Arrange the following radicals in order from least to greatest.               

4√6, 2√15, 3√5, 4√7, 5√3

2. Write the following radicals as mixed radicals in simplest form.

a) 5√8

b) 4√27   

3. Write the following mixed radicals as entire radicals.

a) 2√10

b) 4√6   

4. Simplify.  Do not give the decimal approximation.

a) √25 - √16

b) 3√48 - 4√8 + 4√27 - 2√72         

c) 2√2(3√6 - √3)

d) (2√7 + 3√5)(2√7 - 3√5)   

e) √7/√8

f) -√25/12√5

5. State any restrictions on x, and then solve each equation. For your answer, do not give the decimal approximation.

a) 3√(25+x) = 21                                                               

b) 3+√(4x+1) = 9

c) 3√(9x-2) = 4

6. Some collectors view comics as an investment. The effective rate of interest, r, earned by an investment can be defined by the formula

R = n√(A/P) - 1

where P represents the initial investment, in dollars, that grows to a value of A dollars after is years.

Determine the initial price of a rare comic book that resold for $1139 after two years, earning its owner 18% interest.

7. The amount of energy, P, in watts (W), that a wind turbine with vanes 40 m long generates, is related to the wind speed, S, by the formula

S = 3√(2P/5026.5D)

where D represents the density of the air where the turbine operates. If a wind turbine is built in an area in which the air density is 0.9 kg/m³ and the average wind speed is 8 m/s, determine how much power this turbine can generate.

8. Melinda bought a circular table for her deck. When she placed it on the deck, she concluded that its area was about a quarter of the area of her 5 m by 5 m square deck. Determine the radius of the table to two decimal places. Justify your response.

9. A space station needs to rotate to create the illusion of gravity. A formula for determining the rotation rate to reproduce Earth's gravity is

N = 42/π √(5/r)

where N represents the number of revolutions per minute and r represents the radius of the station in metres.

A station rotates 6.7 times per minute, producing an effect on the interior wall equivalent to Earth's gravity. Determine the radius of the space station.