Find the cube root of 81: 81−−√3
The cube root of 81 is 4.
To find the cube root of 81, you can use the exponentiation method.
Start by writing 81 as a base raised to a power of 3:
81 = 3^4
Now, take the cube root of both sides of the equation:
³√(81) = ³√(3^4)
Next, use the property of exponents that states a^(m*n) = (a^m)^n:
³√(81) = (³√3^4)
Simplify further:
³√(81) = ³√3^(4/3)
Since 4/3 is in the form of a fractional exponent, you can rewrite it as a radical expression:
³√(81) = √(3²)^(1/3)
Using the property of exponents again, you can multiply the exponent inside the parentheses:
³√(81) = √(3^(2 * 1/3))
Simplify further:
³√(81) = √(3^2/3)
Finally, evaluate the radical expression:
³√(81) = √(3^(2/3)) ≈ 3.000
So, the cube root of 81 is approximately 3.
To find the cube root of 81, you can use the exponentiation operator. The exponentiation operator is represented by the ^ symbol, which raises a number to a given power. In this case, to find the cube root of 81, we need to raise 81 to the power of 1/3.
To express the cube root of 81 as an exponent, we can write it as 81^(1/3). Let's calculate it:
81^(1/3) = 4.3267487109 (rounded to 10 decimal places)
Therefore, the cube root of 81 is approximately 4.3267487109.