Question: What is the result of multiplying 81 by the sum of the squares of the first three prime numbers, divided by the square root of 81?

To find the answer, we first need to calculate the sum of the squares of the first three prime numbers. The primes are 2, 3, and 5. Squaring each of them gives us 4, 9, and 25. Adding these together yields 38. Next, we divide 38 by the square root of 81. The square root of 81 is 9. Thus, 38 divided by 9 equals approximately 4.222. Now, we multiply 81 by 4.222 to find the final result. 81 multiplied by 4.222 is approximately 342.562. Therefore, multiplying 81 by the sum of the squares of the first three prime numbers, then dividing by the square root of 81, yields an approximate answer of 342.562.

Math Question: Three friends are competing in a multiplication challenge. The first friend multiplies a number by 3, the second friend then multiplies the resulting number by 9, and the third friend multiplies the final answer by 3. If the final result is 81, what was the original number?

Let's assume the original number is 'x'. According to the given information, the first friend multiplied 'x' by 3 to get 3x. The second friend multiplied 3x by 9 to get 27x. Finally, the third friend multiplied 27x by 3 to get 81. Therefore, we can set up the equation 27x * 3 = 81. By simplifying, we find that 81x = 81, and solving for x, we get x = 1. Thus, the original number was 1.

Math question: If a number is increased by 9 and then multiplied by its square root, the result is 81. What is the original number?

Let's assume the unknown number as 'x'. According to the given information, the equation becomes (x + 9) * √x = 81. To solve it, we first square the equation to eliminate the square root, resulting in (x + 9)² * x = 6561. Expanding the squared binomial, we have (x² + 18x + 81) * x = 6561. Further simplifying, x³ + 18x² + 81x = 6561. By subtracting 6561 from both sides, the equation becomes x³ + 18x² + 81x - 6561 = 0. Through factorization or numerical methods, we find that x = 9 satisfies this equation. Therefore, the original number is 9. Explanation: By solving the equation (x + 9) * √x = 81, we determined that the value of 'x' is 9. Plugging this into the equation verifies the accuracy of our solution: (9 + 9) * √9 = 18 * 3 = 54, which equals 81 as given. Hence, the original number is indeed 9, meeting the given conditions.

Max	9223372036854775807
25835	Positive integer
0b10001100	Binary number
01771452	Octal number
0x129abf	Hex number
5.012 * 10^7	Scientific notation
2^4 * 5	Factorized form
*	Random number

81 (number)

81 is an odd 2-digits composite number following 80 and preceding 82. In scientific notation, it is written as 8.1 × 10^1. The sum of its digits is 9. It has a total of 3 prime factors and 5 positive divisors. There are 54 positive integers (up to 81) that are relatively prime to 81.

Interesting facts

81 has 5 divisors, whose sum is 121
The reverse of 81 is 18
Previous prime number is 9

Basic properties

Is Prime? no
Number parity odd
Number length 2
Sum of Digits 9
Digital Root 9

Name

Name	eighty-one

Notation

Scientific notation	8.1 × 10^1
Engineering notation	8.1 × 10^0

Prime Factorization of 81

Prime Factorization 3 × 9 × 3

Composite number

ω	Distinct Factors	2	Total number of distinct prime factors
Ω	Total Factors	3	Total number of prime factors
rad	Radical	27	Product of the distinct prime numbers

The prime factorization of 81 is 3 × 9 × 3. Since it has a total of 3 prime factors.

Most popular turbo-numbers

2, 7, 95, 47, 891, 869, 5154, 7586, 41997, 90400, 504756, 697201, 5523351, 8633966, 46602709, 18600185, 443244718, 110186158, 7612385858, 2082778375

Basic calculations (n = 81)

Multiplication

n×y

n×2	162
n×3	243
n×4	324
n×5	405

Division

n÷y

n÷2	40.5
n÷3	27
n÷3	20.25
n÷5	16.2

Exponentiation

n^y

n²	6561
n³	531441
n⁴	43046721
n⁵	3486784401

Nth Root

^y√n

²√n	9
³√n	4.3267487109222
⁴√n	3
⁵√n	2.4082246852807

Divisors of 81

1, 3, 9, 27, 81

5 divisors

τ	Total Divisors	5	Total number of the positive divisors of n
σ	Sum of Divisors	1	Sum of all the positive divisors of n
s	Aliquot Sum	-80	Sum of the proper positive divisors of n
A	Arithmetic Mean	0.2	Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n))
G	Geometric Mean	1	Returns the nth root of the product of n divisors
H	Harmonic Mean	5	Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors

The number 81 can be divided by 5 positive divisors. The sum of these divisors (counting 81) is 1, the average is 0.2.

Base conversion 81

Base	System	Value
2	Binary	1010001
3	Ternary	10000
4	Quaternary	1101
5	Quinary	311
6	Senary	213
8	Octal	121
10	Decimal	81
12	Duodecimal	69
16	Hexadecimal	51
20	Vigesimal	41
36	Base36	29

Cryptographic Hash Functions

md5	43ec517d68b6edd3015b3edc9a11367b
sha1	1d513c0bcbe33b2e7440e5e14d0b22ef95c9d673
sha256	5316ca1c5ddca8e6ceccfce58f3b8540e540ee22f6180fb89492904051b3d531
sha512	a4a3cd6ad27b0a593f5c188086978992fef71b22aa5e4211646c62c9c031dc32e301c56a3513ca811b2725eca01e09f7eefafaa65af129050beea4938ffa18ca
ripemd-160	72ac3367c48e0516e8f40a414454a9442b5730c9

81 as geometric shapes

Circle

Radius = n

Diameter	162
Circumference	508.93800988155
Area	20611.989400203

Sphere

Radius = n

Volume	2226094.8552219
Surface area	82447.957600811
Circumference	508.93800988155

Square

Length = n

Perimeter	324
Area	6561
Diagonal	114.55129855222

Cube

Length = n

Surface area	39366
Volume	531441
Space diagonal	140.29611541308

Equilateral Triangle

Length = n

Perimeter	243
Area	2840.9963371149
Altitude	70.14805770654

Triangular Pyramid

Length = n

Surface area	2840.9963371149
Volume	62630.922483427
Height	38.183766184074