What is Cube Root of 306

• Cube root of 306 is written as $\sqrt[3]{306}$ (Radical form).
• $\sqrt[3]{306}$ = $\sqrt[3]{6.7387 \times 6.7387 \times 6.7387}$ = 6.7387
• In the exponential form, the cube root of 306 is expressed as $(306)^\frac{1}{3}$.

Cube Root by Halley's Method

Halley's method is an iterative technique used to find cube roots. To find the cube root of a number using Halley's method, follow these steps:

Its formula is $\sqrt[3]{a} ≈ x \left( \frac{ \left( x^3 + 2 \times a \right) }{ \left( 2 \times x^3 + a \right) } \right)$ where,

• a = number whose cube root is being calculated = 306
• x = integer guess of its cube root.

Let's assume x as 6. Since 306 lies between 216 (cube of 6) and 343 (cube of 7). So, we will consider the closest cube number here, i.e. 7.

Using the above formula & numbers, let's calculate the cube root of 306