Here’s a pretty easy one from me:
x³ + x⁵ = ??
Slightly harder:
Write 7√20 in the form k√5 , where k is an integer.
Even harder:
Simplify fully (2a+b) sqaured
first one is x8 but thats all I know
I recently learned about this,
Convert 1800km/m into m/s
Correct!
kehfbiewuhfidsbfkhfjsdbfj
I only posted twice with it
nice, question, is it km/m, or km/h
km/min
2000000000000000000
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Sorry for the delay. I’m back again. So let’s get on with our lesson on exponents and radicals! 
Large Lesson with Radicals
Just a quick recap: we talked about how exponents that are whole numbers show how many times to multiply the base by itself. If the exponent is negative, then it’s like putting the entire expression on the bottom of a fraction, with the number 1 on the top. To multiply or divide exponents with the same base you add or subtract the value of the exponents.
Now we will discuss “roots” (aka “radicals”). They are the inverse of exponents. The inverse is basically the opposite, like add/subtract, multiply/divide.
They have can have the same notation as exponents, but then the exponent is a fraction. Or they can have the radical symbol:
√
For this expression: 53 =125 The exponent is 3
What does that mean, exactly? It means you multiply 5 by itself 3 times → 5 * 5 * 5 =125
So when figuring out the root, you are working backwards, starting with the larger expression.
53 =125 (forwards)
3√125 = 5 (backwards)
NOTE: 3√125 is the same as 1251/3 (It’s just a different notation)
Starting with the bigger number, you figure out what value can be multiplied by itself 3 times to equal it.
Stop and read entry 248 again, and see if it makes any more sense this time
Technically, the size of the radical can be any value, but in practical use, it’s usually 2 or sometimes 3. It’s so often 2 that if you see √x (the little number on the left appears to be missing), it is understood to be 2. √x = 2√x = x1/2
To solve perfect roots (meaning the answer is a whole number), you can use Prime Factorization.
Take a moment to read through entry 250 of this thread to learn about Prime Factorization
To manipulate roots, you can write them as fractions and treat them just like other exponents. Multiply by adding, divide by subtracting.
There are also some useful properties of radicals that are the same as other exponents. The following is copied from a helpful reference webpage: Radical
(Do not worry about all the variables: x, y, z, n, m. All you need to understand is that in any single equation, each letter represents some number. So you could pretend the x = 1 so when you see x on each side of the equals sign, just imagine it is a 1. Each of these variables is just a placeholder for a number, but it is always the same number when in the same equation.)
Properties of radicals
There are many properties of radicals and exponents that can be helpful for simplifying expressions or solving equations. Below are some of them.
(1) 
(2) 
Note: While the properties above might seem like they could apply to addition and subtraction, it is important to note that they do not apply to addition and subtraction. We cannot separate addition and subtraction under a radical the same way we do multiplication and division.
(3) If 
then 
(z must be ≥ 0 for even n)
(4) 
(if x ≥ 0 or if n is odd)
(5) 
(when x < 0 and n is even)
(6) 
So what might that look like without variables? Let’s look at line 1:
We could pick some numbers to go in there pretty much at random. So, n = 2 x = 1 y = 4
n√xy = n√x * n√y
Put in the numbers
2√(1*4) = 2√1 * 2√4
All of the properties here work with both exponents and radicals. They mean that if an expression is multiplied or divided and you have an exponent or a radical over all of it, you can separate them out and solve them individually.
(2/3)2 is 2/3 * 2/3 = 4/9
You could also write it out like this:
22 / 32 = 4/9
or 3√(8/27) = 3√8 / 3√27 = 81/3 / 271/3 = 2/3
You try. First write each equation in “radical” form (with the little box on the left side) and in “exponent” form (with the fraction exponent). Then solve whichever way you prefer.:
10001/3 = ?
√130 = ?
2√(24 + 32) = ?
34 / √3 = ?
i want to make sure I understand this correctly before i go putting wrong answers lol
radicals are just like exponents, but dividing.
so for example, 2√60 would be15, since 60 / 2 = 30, and 30 / 2 is 15
lol dont know why i think this
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if a helicopter flew straight with a slack rope attached (no weight on the end) what shape would it make
yes in a way
Radicals work like exponents, and exponents are multiplying the number by itself, so technically for the radical, you need the number that you multiply it by itself to get the number. For example, if you need to get the square root of 9, written this way √9, you need to find the number that you multiply by itself once (having two of it) that gives you 9, 3 * 3 gives you 9 so the square root for 9 would be 3.
So if you multiply 15 by itself, it won’t give you 60, it will give you 225
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I don’t know, but I do wonder what would happen if an airplane flew a few feet off the ground and flew straight. If they flew literally straight (not up any), would they come out of the atmosphere? Would the airplane not circle the Earth, but just fly straight out?
Does @DoesNotCompute have an easy to understand expiation to this?
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so the square root of 12 would be 6, correct?
Not really, 6 * 6 is not 12
The square root of 12 is a decimal
Try finding the square root of 49
Not for vanessa
7 this was almost invis
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Does anyone know what the linear scale factor and area scale factor is?
so basically in simple words, if you have a line that is 4 cm long and another line that is 8 cm long, the scale factor from the shorter line to the longer one would be 8/4 = 2
in triangles for example, if you have a triangle with a base length of 5 and another triangle with a base length of 15, then the scale factor would be 3 also from the smaller to the bigger
i think the area scale factor is the same idea
from Google:
Scale factors can be used to compare lengths and areas . Scale factors are calculated differently for area. This table shows that if a shape’s lengths are increased by a scale factor of 2, the surface area will be increased by a scale factor of 4. To calculate the area scale factor, square the length scale factor.
Well, we are talking about helicopters, not airplanes, Lol, and helicopters use air stuff blah blah blah to fly, so when the air gets thiner, it flies worse I think…
The answer is 7
200000000000
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Yess, try DoesNotCompute’s now
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