Questions on Algebra: Radicals -- complicated equations involving roots answered by real tutors!

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Question 1206442: I'm working on half-angle identities for trigonometry and I keep getting the wrong answer, or possibly in a different form than the book's answer.
I'll just ask about the answer which is basically rationalizing a root problem (with a fractional root within it).
I keep getting stuck on an intermediary step, as follows, from the solution in the book:
sqrt(1+sqrt(5))/sqrt2
which gives the solution:
sqrt(50-10sqrt(5))/10
I know I'm messing up with rationalizing the denominator and I can't figure it out.
I ran the plain text radicals above in Wolfram Alpha and it comes out basically as the problem/solution in the book.
Any help would be greatly appreciated.
Click here to see answer by greenestamps(13200)

Question 1206539: (7x^(-6))^(2)

Click here to see answer by math_tutor2020(3817)

Question 1069865: Sarah is collecting recyclables for a science project. On the first day she collects 35 recyclable objects. On the second day she has a total of 52 recyclables. On the third day she has a total of 69 recyclables. Determine if the scenario describes an arithmetic or a geometric sequence. Then, write the recursive formula for the sequence described.

Click here to see answer by mananth(16946)

Question 1207630: Find the real solutions of each equation.

rt{10 + rt{x}} = rt{x}
Click here to see answer by Edwin McCravy(20055)

Question 1207632: Find the real solutions of each equation.

Let rt = root

1. x^2 - 3x - rt{x^2 - 3x} = 2

2. 3x^(3/4) + 5x^(2/3) - 2 = 0
Click here to see answer by ikleyn(52781)

Question 1207631: Find the real solutions of each equation.

1. x^(3/4) - 9x^(1/4) = 0

2. Let rt = root

rt{100 - rt{x}} = rt{x^2}

Note: IF there are no real solutions, say so.
Click here to see answer by ikleyn(52781)

Question 1207660: Find the real solutions of the equation.

x^2 + 3x + sqrt{x^2 + 3x} = 6

I was to able reduce it to look like this:

x^2 + 3x = (x^2 + 3x - 6)^4

Stuck here ....
Click here to see answer by ikleyn(52781)

Question 1207658: Find the real solutions of the equation.
(5x^2 - 6)^(1/4) = x
I found x to be -sqrt{6} and sqrt{6}.
The textbook answer is x = sqrt{2} and x = sqrt{3}.
Help.
Click here to see answer by Theo(13342)

Question 1207659: Find the real solutions of the equation.

This one threw me into a loop.

4x^(1/2) - 9x^(1/4) + 4 = 0
Click here to see answer by ikleyn(52781)

Question 1207668: The distance to the surface of the water in a well can sometimes be found by dropping an object into the well and measuring the time elapsed until a sound is heard. If x is the time (measured in seconds) that it takes for the object to strike the water, than x will obey the equation s = 16x^2, where s is the distance (measured in feet). It follows that x = sqrt{s}/4.
Suppose that y is the time it takes for the sound of the impact to reach your ears. Because sound waves are known to travel at a speed of about 1100 feet per second, the time y to travel the distance s will be y = s/1100. Now x + y is the total time that elapses from the moment that the object is dropped to the moment that a sound is heard.
We have the equation TOTAL TIME ELAPSED = (sqrt{s}/4) + (s/1100).
Find the distance to the water's surface if the total time elapsed from dropping a rock to hearing it hit water is 4 seconds.

Wow! That's a mouth full.

I rearranged the original equation to be
s + 275(sqrt{s}) = 4400

Stick here....
Click here to see answer by ikleyn(52781)

Question 1207666: Find the real solutions by factoring.

x^2 + sqrt{3}x^2 - 3 = 0

Let x^4 = (x^2)^2

Let u = x^2

u^2 + sqrt{3}x - 3 = 0

Stuck here....

Can I use the quadratic formula?
Click here to see answer by ikleyn(52781)

Question 1207669: A civil engineer relates the thickness T, in inches, and height H, in feet, of a square wooden pillar to its crushing load L, in tons, using the model
T = [(LH^2)/25)]^(1/4).
If a square wooden pillar is 4 inches thick and 10 feet high l, what us the crushing load?

Here is my set up:

4 = [(L(10)^2)/25)]^(1/4).

Is this correct?

Thanks.
Click here to see answer by ikleyn(52781)

Question 1207665: Find the real solutions by factoring.
x(x^2 - 3x)^(1/3) + 2(x^2 - 3x)^(4/3) = 0
I factored out (x^2 - 3x)^(1/3).
(x^2 - 3x)^(1/3)[x + 2(x^2 - 3x)^(4/9)]
Stuck here....
Click here to see answer by ikleyn(52781)

Question 1207633: Find the real solutions of each equation. Use a calculator to express any solutions rounded to two decimal places.

1.

2.
Click here to see answer by semsee45(1)

Question 1208223: simplify sqrt(-42) by sqrt(-6)

Click here to see answer by Edwin McCravy(20055)

Question 1208758: Find an approximation for squareRoot17 without a calculator. Round to nearest thousandth.
Click here to see answer by math_tutor2020(3817)

Question 1208840: Find the real solutions of the radical equation.

x^(3/4) - 9[x^(1/4)] = 0
Click here to see answer by josgarithmetic(39617)

Question 1208839: Find the real solutions of the radical equation.

sqrt{(10+ 3•sqrt{x})} = sqrt{x}

Note: (10 + 3•sqrt{x}) lies inside a bigger radicand.
Click here to see answer by Edwin McCravy(20055)

Question 1209005: What is the smallest positive integer n such that \sqrt[4]{675 + n} is an integer?

Click here to see answer by ikleyn(52781)

Question 1209033: Evaluate the following expression:
\left( \frac{16}{9} \right)^{2/3} \cdot \left( \frac{4}{3} \right)^{3/4} \cdot \left( \frac{81}{2} \right)^{5/3} \cdot \left( \frac{27}{2} \right)^{1/12} \cdot \left( \frac{1}{9} \right)^{1/4}
Click here to see answer by greenestamps(13200)

Question 1209031: Simplify sqrt(17) * sqrt(12) * sqrt(16) * sqrt(85) * sqrt(18) * sqrt(51).
Click here to see answer by greenestamps(13200)

Question 1209125: Simplify the expression
\frac{1}{\sqrt{36} - \sqrt{27}} - \frac{1}{\sqrt{27}} - \sqrt{18} + \frac{1}{\sqrt{18}} - \sqrt{9}.
Click here to see answer by mccravyedwin(407)

Question 1209124: Simplify the expression
\frac{3}{\sqrt{2}} * \frac{1}{\sqrt{8}} * \frac{6}{\sqrt{32}}.
Click here to see answer by mccravyedwin(407)

Question 1209030: Simply sqrt(2) \cdot sqrt(6) \cdot sqrt(110) \cdot sqrt(47) \cdot sqrt(52) \cdot sqrt(550).
Click here to see answer by yurtman(42)

Question 1209030: Simply sqrt(2) \cdot sqrt(6) \cdot sqrt(110) \cdot sqrt(47) \cdot sqrt(52) \cdot sqrt(550).
Click here to see answer by greenestamps(13200)

Question 1209233: Simplify 1/(sqrt(2) + 2 + sqrt(3)) + 1/(sqrt(2) - 2 - sqrt(3)).
Click here to see answer by Edwin McCravy(20055)

Question 1209395: Compute the sum
\frac{1}{\sqrt{36} + \sqrt{39}} + \frac{1}{\sqrt{42} +\sqrt{45}} + \frac{1}{\sqrt{45} + \sqrt{49}}
Click here to see answer by ikleyn(52781)

Question 1209657: Determine the sum of all real numbers x satisfying
(x^2 - 6x + 4)(x^2 - 8x + 5) = 1.
Click here to see answer by proyaop(69)

Question 1209867: Express 2 + sqrt(2) + 1/(2 + sqrt(3)) + 1/(sqrt(5) - 2) in simplest form.
Click here to see answer by Edwin McCravy(20055)

Question 1209873: Find all x such that
sqrt{3x^2 + 2x + 1} + sqrt{3x^2 + 2x - 3} = 20.

Click here to see answer by CPhill(1959)

Question 1209873: Find all x such that
sqrt{3x^2 + 2x + 1} + sqrt{3x^2 + 2x - 3} = 20.

Click here to see answer by ikleyn(52781)

Question 1209872: Simplify \frac{6 \sqrt{2]}{\sqrt{2} - \sqrt{3} - \sqrt{5}}
Click here to see answer by CPhill(1959)

Question 1209888: Compute
\frac{\{\sqrt{3}\} - 4 \{\sqrt{5}\}}{\{\sqrt{3}\}^2 + \{\sqrt{2}\}^2}.
Click here to see answer by CPhill(1959)

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