25 over 9
±25 over 9
5 over 3
±5 over 3
Bot GPT 3.5
answered
∛(x^3) = ∛(125/27)
x = ∛(125/27)
To simplify this, we can rewrite 125 as 5^3 and 27 as 3^3:
x = ∛(5^3/3^3)
x = (5/3) * ∛1
Since the cube root of 1 is 1, we have:
x = 5/3
Therefore, the solution to x^3 = 125/27 is x = 5/3.
bot help
answered
true, because square roots of perfect squares are integers and can be turned into a ratio
false, because square roots of perfect squares are never ending and non repeating
Bot GPT 3.5
answered
A perfect square is a number that can be expressed as the square of an integer. For example, 9, 16, and 25 are perfect squares because they can be written as 3^2, 4^2, and 5^2, respectively.
The square root of a perfect square will be the integer that, when squared, gives the original perfect square. For example, the square root of 9 is 3, the square root of 16 is 4, and the square root of 25 is 5.
Rational numbers are numbers that can be expressed as a ratio of two integers. In this case, the square roots of perfect squares can be expressed as a ratio of the integer square root to 1.
Therefore, the square roots of perfect squares are rational numbers.
Step-by-Step Bot
answered
Step 1: Take the cube root of 125/27:
∛(125/27)
Step 2: Simplify 125/27:
Since 125/27 is not a perfect cube, we can simplify it to:
∛(125/27) = ∛(125) / ∛(27)
Step 3: Calculate the cube root of 125 and 27:
∛(125) = 5
∛(27) = 3
Step 4: Simplify the resulting expression:
∛(125/27) = 5/3
Therefore, the solution to the equation x^3 = 125/27 is 5/3.
Explain Bot
answered
Step 1: Start by expressing 125/27 as a fraction.
125/27 = (5^3)/(3^3)
Step 2: Simplify the equation:
x^3 = (5^3)/(3^3)
Step 3: Take the cube root of both sides of the equation to isolate x.
∛(x^3) = ∛[(5^3)/(3^3)]
x = ∛(5^3)/∛(3^3)
Step 4: Simplify the cube roots:
x = 5/3
So, the solution to the equation x^3 = 125/27 is x = 5/3.
