Simplify the square root of 5 times the cube root of 5
To simplify the expression, we can rewrite it as a single radical:
√5 * 5^(1/3)
Since both terms have 5 as a common factor, we can factor it out:
5 * (√5 * (5^(1/3) / 5))
Now, let's simplify the cube root of 5:
5 * (√5 * 5^(1/3) / 5)
= 5 * (√5 * (∛5^3 / 5))
= 5 * (√5 * (∛125 / 5))
The cube root of 125 is 5 because 5 * 5 * 5 = 125.
Now we have:
5 * (√5 * (5 / 5))
= 5 * (√5 * 1)
= 5 * √5
Therefore, the simplified form of the expression is 5√5.
Simplify the square root of 5 times the cube root of 5.
five to the five sixths power
five to the one sixth power
five to the two thirds power
five to the seven sixths power
To simplify the square root of 5 times the cube root of 5, we can express both terms with the same index.
The square root of 5 can be written as 5^(1/2).
The cube root of 5 can be written as 5^(1/3).
Combining these expressions, we have:
5^(1/2) * 5^(1/3)
To simplify this, we can combine the exponents:
5^(1/2 + 1/3) = 5^(3/6 + 2/6) = 5^(5/6)
Therefore, the simplified expression is "five to the five-sixths power."
The number of users of the internet in a town increased by a factor of 1.01 every year from 2000 to 2010. The function below shows the number of internet users f(x) after x years from the year 2000:
f(x) = 3000(1.01)x
Which of the following is a reasonable domain for the function?
0 ≤ x ≤ 10
2000 ≤ x ≤ 2010
0 ≤ x ≤ 3000
All positive integers
The reasonable domain for the function f(x) = 3000(1.01)^x is determined by the context of the problem.
Since the function represents the number of internet users after x years from the year 2000, a reasonable domain for x would be the range of years mentioned in the problem statement, which is from 2000 to 2010.
Therefore, the reasonable domain for the function is: 2000 ≤ x ≤ 2010.
To simplify the square root of 5 times the cube root of 5, we can multiply the two terms.
√5 * ∛5
To combine the terms, we need to convert them to a common index. The square root can be written as a cube root with an index of 2:
√5 = ∛(5^2)
Now we can multiply the two terms:
∛(5^2) * ∛5
To simplify further, we can combine the bases inside the cube roots:
∛(5^2 * 5)
Simplifying the expression inside the cube root:
∛(25 * 5)
∛125
So the simplified expression is ∛125.
To simplify the expression "square root of 5 times the cube root of 5," we can use the properties of radicals.
First, let's break down the expression into separate radicals:
√5 * ∛5
Next, we can simplify each radical separately.
The square root of 5 (√5) cannot be simplified further because 5 is a prime number.
The cube root of 5 (∛5) is also simplified because there are no perfect cubes that can be extracted from 5.
Therefore, the simplified form of the expression "square root of 5 times the cube root of 5" is:
√5 * ∛5