What is the cube root of 407 squared? On this page, we will show you three methods you can use to solve this math problem. However, before we begin, let us show you the mathematical presentation of cube root of 407 squared:
(∛407)²
Method 1:
In this first method, we start by taking the cube root of 407, and then square the result. In other words, we follow the rule of PEMDAS and solve what is inside the parentheses first, before the exponent. Here is the math and the answer:
∛407 ≈ 7.410795
7.410795² ≈ 54.91988
(∛407)² ≈ 54.91988
Method 2:
In the second method, we start by squaring 407 and then take the cube root of the result. This method is possible because of this rule: ∛a × ∛b = ∛(a × b). Here is the math and the answer to do it this way:
407² = 165649
∛207936 ≈ 54.91988
(∛407)² ≈ 54.91988
Method 3:
In the third and final method, we convert the problem to a base with an exponent and solve it. This method is possible because (∛x)² is equal to x raised to the power of 2/3. Here is the math and the answer to do it this way:
(∛407)² = 407²/³
407²/³ ≈ 54.91988
(∛407)² ≈ 54.91988
Bonus:
By popular demand, we have also calculated the simplest radical form of the cube root of 407 squared:
(∛407)² = ∛165649
Cube Root Squared
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