Radical Functions, algebra homework help

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OPEN ENDED Write a sum of three radicals that contains two like terms. Explain how you would combine the terms. Defend your answer.
Writing in Math Refer to the information on page 435 to explain how rational exponents can be applied to astronomy. Explain how to write the formula in radical form and simplify it.
Writing in Math Refer to the information on page 442 to describe how the cost and the number of units manufactured are related. Rewrite the manufacturing equation C = 10n2/3 + 1500 as a radical equation, and write a step-by-step explanation of how to determine the maximum number of chips the company could make for $10,000.

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-6 Rational Exponents deas GET READY for the Lesson spressions alional nents in radical and vice vers lity expressions paneral or Lallom. Astronomers refer to the space around a planet where the planet's gravity is stronger than the Sun's as the sphere of influence of the planet The radius r of the sphere of influence is given by the formula M, ľ =D M. where M, is the mass of the planet, M, is the mass of the Sun, and D is the distance between the planet and the Sun. Rational Exponents and Radicals You know that squaring a number and taking the square rool of a number are inverse operations. But how would you evaluate an expression that contains a fractional exponent such as the one above? You can investigate such an expression by assuming that fractional exponents behave as integral exponents. (12) – 52. p write the square as multiplication, = 61+1 Add the exponents =bi or b Simplify Thus, bż is a number whose square equals b. So b2 = V. KEY CONCEPT i = 0. Wands For any real number b and for any positive integer a. except when b < 0 and n is even. Bample 8 = V8 or 2 EXAMPLE Radical and Exponential Forms O. Write ai in radical form b. Write Vy in exponential form aiva Deletion of Definition of - contai 10. IA A mcyuall GET READY for the Lesson Computer chips are made from the element silicon, which is found in sand. Suppose a company that manufactures computer chips uses the 10n formula C = 10n3 + 1500 to estimate the cost C in dollars of producing a chips. This can be rewritten as a radical equation. Solve Radical Equations Equations with radicals that have variables in the radicands are called radical equations. To solve this type of equation, raise each side of the equation to a power equal to the index of the radical to eliminate the radical. It is very important that you check your solution. Sometimes you will obtain a number that does not satisfy the original equation. Such a number is called an extraneous solution. EXAMPLE Solve Radical Equations Solve each equation. a. Vx+1+2=4 Vx+1 +2=4 Original equation Vx+1 = 2 Subtract 2 from each side to isolate the radical. (Vx + 1)2 = 22 Square each side to eliminate the radical. x + 1 = 4 Find the squares. x= 3 Subtrad 1 from each side. CHECK Vx+1+2=4 Original equation V3+1 +2 = 4 Replace x with 3. 4= 4 Simplify. The solution checks. The solution is 3. b. Vx-15 = 3- V* Vx-15 = 3-V Original equation (Vx - 15)2 = (3 - Vx) Square each side. * - 15 = 9 - 6VX +* Find the squares. -24 = -6 Isolate the radical. Divide each side by -6.
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Explanation & Answer

Here are the answers, please tell me if you have any problem

1- A sum of three radicals that contains two like terms:
Example: √5 + 7√3 + 5√3
In this example, the like terms are 7√3 + 5√3
Think of radicals as "variables" and put 𝑎 = √3, you could read the example like:
√5 + 7𝑎 + 5𝑎
we combine the terms like √5 + 12𝑎, then √5 + 7√3 + 5√3 = √5 + 12√3

2- To explain how rational exponents can be applied to astronomy:
From page 435, the formula: 𝑟 = 𝐷(

𝑀𝑝 2
𝑀𝑠

)5 can be applied in astronomy to get the

radius of the sphere of the influence of a plant (𝑟) where: 𝐷 is the distance
between the plant and the sun, 𝑀𝑝 is the mass of the plant, 𝑀𝑠 is the mass of the
sun, in this equation the term (
To write the formula: 𝒓 ...