Imaginary numbers (i)
i^2
Hint: sqrt(-1) = i
Simplify sqrt(54)
Hint: Think of how 27 is divisible by nine and three. Nine is able to be square-rooted, but three is not, so you square root nine and leave the three alone, resulting in 3 * sqrt(3), which is sqrt(27) in its most simplified form.
sqrt(54)
sqrt(9) * sqrt(6)
3 * sqrt (6)
4!
Hint: 10! = 10*9*8*7*...*3*2*1
4! = 4*3*2*1 = 24
What is this number called?: 10^6
Hint: "^" means "to the power of," and for every ten you multiply by itself, it adds a zero. For example, 10^1 is ten, which has a single zero. 10^0 is one, as it has no zeroes. 10^5 is 100,000 according to the pattern, so just multiply 100,000 by ten for the answer.
A million
What is 6^6^6?
1.03144248 with 28 extra digits after. This can also be notated as 1.03144248e28, which is approximately 1.03^34; any variations of this answer are allowed.
-i^2
1
2 * sqrt(11)
1!
1
What is this number called?:
10^303
A centillion
What is 0^0 equal to?
It results in NaN (Not a Number). The way zeroed exponents work goes like this:
The exponent number for multiples of ten determines how many zeroes there are after the 1. For example, 10^1 is 10; 10^0 is one; and 10^-1 is 0.1. Therefore, 0^0 is impossible, as that means there are no zeroes... which is impossible for a zero.
3i+22i
25i
Simplify sqrt(64)
8
(43! / 41!)
Hint: When dividing factorials, you remove all numbers in the bottom factorial that happen are in the top factorial. An example is (3! / 2!), which is 3*2*1 / 2*1, resulting in just 3; doing this the long way would take ages for (1000! / 999!), because it is lengethened out to 1000 * 999 * 998 * ... * 3 * 2 * 1 divided by 999* 998 * 997 * ... * 3 * 2 * 1, so just do the easy way.
43! / 41!
43*42
1806
What is this number called?:
10^10^100
A googolplex
This number was created by 10^googol, as googol is equal to 10^100, thus creating a googolplex.
What is (4!)^5 equal to?
(4!)^5
(4*3*2*1)^5
24^5
7,962,624
3i * 7
21i
Simplify sqrt(125)
5 * sqrt(5)
3! * 4!
(3*2*1)*(4*3*2*1)
6*24
144
True or False:
A googolplexidex is equal to 10^10^10^10^100.
This is False. It actually equals a googolduplexidex. Meanwhile, 10^10^10^100 is a googolplexidex.
(4!)^3
24*24*24
576*24
13824
28i / 4i
7
Is this number a surd or a radical?: sqrt(256)
Hint: Surds have a number before the root; Radicals give a whole number.
This is equal to 16, so this is a radical.
(3!)!
(3*2*1)!
6!
(6*5*4*3*2*1)!
720
WARNING!: This number is written in Hyper-E Notation. An example is listed below the question.
What is this number called?: E100#100
Hint: Hyper-E Notation is another way of writing larger numbers. For example, E9#1 is 1 followed by 9 zeroes, or one billion. But don't confuse it with E1#3, because this is actually equal to 10^10^10, which is known as a trialogue. Also, don't expect to know this. Unless you do.
This is a grangol. It's larger than a giggol (E1#100), but smaller than a grangoldex (E100#100#2).
(5!)(i^3)
(5*4*3*2*1)(-1*i)
120(-1i)
-120i