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Square Root Problems

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1. for g(x) = sqrt(x^2 - 20), find g(5)
2. find the domain of f(x) = sqrt(x) + 6
3. the cost of making clocks is c = 121sqrt(n + 36). what is c when no clocks are made?
4. find the following: sqrt((14y)^2)
5. simplify: y^(4/3)/y^(5/6)
6. graph: f(x) = -sqrt(2 - x)
7 - 15. multiply and simplify expressions involving square roots, fractions, exponents, and i
16 - 18. solve equations involving square roots
19 - 20. word problems

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g(5) is the value of the function when x = 5. To find it, just plug 5 in for x:

g(x) = √(x2 - 20)
g(5) = √((5)2 - 20)
g(5) = √(25 - 20)
g(5) = √5 = 2.236

The domain of f(x) is those values of x for which f(x) is a valid function.

The only part of this function that would affect the domain is the √x part. You can't take the square root of a negative number, but you can take the square root of 0, so the function f(x) is only valid when x is greater than or equal to 0.

The domain of f(x) is all real numbers x, such that x ≥ 0. This can be written in interval notation as [0, ∞).

The phrase "no clocks are produced" means that n = 0. Plug n = 0 into the problem, and solve for the cost, c:

c = 121√(n + 36)
c = 121√(0 + 36)
c = 121√36
c = 121*6
c = 726

The cost of manufacturing zero clocks is 726 (dollars?).

Let's think of a hypothetical example. Suppose 14y was equal to -1. If you square it, you get (14y)2 = 1. Then, if you take the square root of that, you get √(14y)2 = 1, which is the opposite of what you started with (i.e. -14y).

Now, suppose 14y was equal to 1. If you square it, you get (14y)2 = 1. Then, if you take the square root of that, you get √(14y)2 = 1, which is the same as what you started with (i.e. 14y).

In general, if 14y is negative (which would mean y was less than 0), √(14y)2 = -14y. If 14 y is positive (which would mean y was greater than 0), √(14y)2 = -14y. Finally, if 14 y is equal to 0 (which would mean y was equal to 0), √(14y)2 = 14y.

Therefore, √(14y)2 = 14y or -14y

When you divide things with exponents, you subtract the bottom exponent from the top exponent:

y4/3/y5/6 = y(4/3 - 5/6) = y(8/6 - 5/6) = y3/6 = y1/2

The answer is y1/2, but you should know that this is the same as √y.

Remember that you can't take the square root of a negative number, so the term ...

Solution Summary

This problem set consists of 20 algebra questions involving square roots. The solution provides complete, step-by-step explanations of how to solve the problems as well as all of the answers.

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