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

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Question 627294: Use the laws of exponents to simplify.
5/4
9.1
________
2/3
9.1

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Question 627353: (radical sign)2x +11= x + 7
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Question 627353: (radical sign)2x +11= x + 7
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Question 627368: √25x - 25
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Question 627390: The function f(x)=6.75 X+12 models the amount, F(x), in billions of dollars of new student loans x years after 1993. According to the model, in what year is the model is the amount loaned expected to reach $45.75 billoin?

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Question 627206: solve x= sqrt (x-2) + 2
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Question 627665: Please help me solve and put in lowest terms;
sqrt%2896%29-4+sqrt%28+24%29

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Question 627666: Please help me solve an put in lowest terms:
%282%2Asqrt%283%29+%2B+3%29%282%2Asqrt%283%29+-+3%29

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Question 627666: Please help me solve an put in lowest terms:
%282%2Asqrt%283%29+%2B+3%29%282%2Asqrt%283%29+-+3%29

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Question 627664: Please help solve and put in lowest terms:
70+sqrt+28%2F14+sqrt+7

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Question 627663: Please help simplify and write in lowest terms:
3 sqrt 343

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Question 627685: Consider the three points A=(-6,6), B=(-4,10), and C=(-2,9). Find the length of each side of the triangle ABC.?

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Question 627878: How can you plug your answer in to check your work?
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Question 628044: i dont understand how to add and subtract radicals for example
sqrt(96)+sqrt(150)-sqrt(54)

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Question 628188: What is the simpliest form of √ 567w^12
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Question 628226: I have a test that is coming up this Sunday and I need to know how to solve these type of Radical word problems. Can someone please help me with these questions and scenarios?
Note: For any decimal answers, please round to two decimal places.
The speed of a tsunami approaching land depends on the depth of the water the tsunami is in. So, the speed of the tsunami changes as is approaches the shore. The speed (in meters per second) of a tsunami in water that is d meters deep is given by s=3.13 square root d.
PROBLEM SHOW YOUR SOLUTIONS HERE
1. Solve this equation for d
2. By looking at the equation, would you expect tsunamis to travel faster or slower as they get closer to the shore (in shallower water)?

3. Find the speed of a tsunami in a depth of 500 m

4. Find the speed of a tsunami in a depth of 100 m
5. Do the answers to problems 3 and 4 confirm your expectation from problem 2? Do Tsunami’s travel faster or slower in shallow water?

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Question 628251: Can someone please help me to solve these radicals. I'm confused as to how these should be set-up.
I have a test that is coming up this Sunday and I need to know how to solve these type of Radical word problems. Can someone please help me with these questions and scenarios?
Note: For any decimal answers, please round to two decimal places.

If a satellite is orbiting earth, it’s distance from the center of earth is dependent upon it’s orbital velocity (speed at which it orbits the earth). The distance, r, that the satellite is from the center of the earth can be found using this equation: r=Kv^-2 for v , where K is a constant and v is the satellite’s orbital velocity.
1. Solve the equation for v. (Remember to use the negative exponent rule to write the expression with positive exponents before solving for v)

2. Suppose that a satellite orbiting at a velocity of 4.93 km/s has an altitude such that the distance from the center of the earth to the satellite is 16378 km. Find the value of K that makes the equation true.

3. Use the value of K you found in the previous problem to determine the altitude of a satellite orbiting at a velocity of 5.4 km/s
Note: The altitude of the satellite is its height above the surface of the earth. The radius (distance from the center to the surface) of the earth is 6378 km, you will need this number to find the altitude of the satellite once you have found a value for r.
4. Find the orbital velocity of a satellite with an altitude of 15,000 km above the surface of the earth.

[Be sure to calculate r before plugging it into the equation]

Click here to see answer by richwmiller(17219) About Me 

Question 628258: Can someone please help me to solve these radicals. I'm confused as to how these should be set-up. I have a test that is coming up this Sunday and I need to know how to solve these type of Radical word problems. Can someone please help me with these questions and scenarios?
Note: For any decimal answers, please round to two decimal places.
If a satellite is orbiting earth, it’s distance from the center of earth is dependent upon it’s orbital velocity (speed at which it orbits the earth). The distance, r, that the satellite is from the center of the earth can be found using this equation: r=Kv^-2 , where K is a constant and v is the satellite’s orbital velocity.
1. Solve the equation for v. (Remember to use the negative exponent rule to write the expression with positive exponents before solving for v)
2. Suppose that a satellite orbiting at a velocity of 4.93 km/s has an altitude such that the distance from the center of the earth to the satellite is 16378 km. Find the value of K that makes the equation true.
3. Use the value of K you found in the previous problem to determine the altitude of a satellite orbiting at a velocity of 5.4 km/s
Note: The altitude of the satellite is its height above the surface of the earth. The radius (distance from the center to the surface) of the earth is 6378 km, you will need this number to find the altitude of the satellite once you have found a value for r.
4. Find the orbital velocity of a satellite with an altitude of 15,000 km above the surface of the earth.
[Be sure to calculate r before plugging it into the equation]

Click here to see answer by Alan3354(69443) About Me 

Question 628296: I am having a problem with this question. I know that yes it is possible I think to have radicals with another root besides a square root, but am unsure as to how it is written. Thank you for your help!
Is it possible to have radicals with another root besides a square root? If possible, how do we write that radical expression?

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Question 627290: Add. Simplify by collecting like radical terms if possible.
8√72+9√32

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Question 627885: Simplify: x^4-3x^3/x^2-9
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Question 628329: The length of a rectangle is 4 meters longer than the width. If the area is 29 square meters, find the rectangles dimensions. Round to the nearest tenth of a meter.
I know you are only going to send me the answer, but how you got the answer would help me to understand how to solve a problem like this if I see it again. Thanks.

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Question 628405: Factor the expression x + 13√x + 12
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Question 628334: A football is kicked straight up from a height of 4 feet with an initial speed of 50 feet per second. The formula H= -16t squared +50t+4 describes the ball's height above the ground, h, in feet, t seconds after it was kicked. How long will it take for the football to hit the ground?
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Question 628471: I need help with solving this problem and it says to use the distributive laws of exponents to simplify. 2^(3/4)*2^(7/8)
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Question 628473: This is very confusing to me and I need help, Please.
Find the following. 20sqrt-2^20

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Question 628473: This is very confusing to me and I need help, Please.
Find the following. 20sqrt-2^20

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Question 628477: I need help with this. The problem states to use rational exponents to writ
√3:(x)*√5:(4x)as a single radical expression and I just don't understand this problem at all.

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Question 628490: Hi! Please help me solve this in the simplest radical form: +sqrt%2828x%5E2y%5E3%29+

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Question 628423: 5divided by x plus 6 divided by x squared over 25 divided by x squared minus 36 divided by x
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Question 628253: Can some one please help me to solve these radical expression and help me to decide if they have a solution. If the radical has no solution can you please explain why? Thanks in advance for your help.

1. Solve. Sqrt x=-3 If the equation does not have a solution, explain why.

2. Solve. Sqrt x+5= Sqrt 2x+8. If the equation does not have a solution, explain why.

3. Solve. x-3= Sqrt 17-4x. If the equation does not have a solution, explain why.

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Question 627877: How do you simplify √16x^5 + y^4 + z^2
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Question 628861: use rational exponents to write x^1/2y^13z^1/8 as a single radical expression
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Question 629008: Find the x-intercept(s) of the graph of the function without graphing the function.
+f%28x%29+=+sqrt%282x%2B21%29-+sqrt%282x%29-3+

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Question 629009: Find the x-intercept(s) of the graph of the function without graphing the function.
+f%28x%29+=+sqrt%282x%2B21%29-+sqrt%282x%29-3+

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Question 629040: I'm not sure of exactly how to work this problem and I need some help...Please.
The question states:
What does it mean to refer to a 20-in TV or a 25-in TV set? Such units refer to the diagonal of the screen. A 20-in TV set also has a width of 16 inches. What is it's height?
My other question is I need help with these two problems also.
sqrtx^2-8x+16 and the other one is a word problem.
It states: The formula r=2sqrt 5L can be used to approximate the speed of r, in miles per hour, of a car that has left skid marks of length L, in feet. How far will a car skid at 70 mph?

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Question 629057: 1. sqrt (45x-90) + sqrt (5x-10)=

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Question 629309: |x|=6
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Question 629308: 3x^2 -6x+1=0
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Question 629311: (4+8i)(4-8i)
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Question 629380: Use rational exponents to write as a single radical expression. Assume that all variables represent positive real numbers.
The 5 root of 3 multiplied by the cube root of z.

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Question 629523: square root of 48 x to the power of 3 y to the power of 5 over the square root of 18 x to the power of 5
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Question 629689: %282sqrt%283%29%2B3%29%282sqrt%283%29-3%29
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Question 629688: +4sqrt%2864x%5E3y%5E7z%5E4%29
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Question 629788: how do you solve square root of 5 times the square roots of 2 minus square root of 90, forgot the rules
how do you find 8% of 5%
thanks!

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Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955, 8956..9000, 9001..9045, 9046..9090, 9091..9135, 9136..9180, 9181..9225, 9226..9270, 9271..9315, 9316..9360, 9361..9405, 9406..9450, 9451..9495, 9496..9540, 9541..9585, 9586..9630, 9631..9675, 9676..9720, 9721..9765, 9766..9810, 9811..9855, 9856..9900, 9901..9945, 9946..9990, 9991..10035, 10036..10080, 10081..10125, 10126..10170, 10171..10215, 10216..10260, 10261..10305, 10306..10350, 10351..10395, 10396..10440, 10441..10485, 10486..10530, 10531..10575, 10576..10620, 10621..10665, 10666..10710