Solve for Cube Root

In mathematics, a cube root of a number, denoted (^3sqrt (x) or x^1/3, is a number such that a³ = x. All real numbers have exactly one real cube root and a pair of complex conjugate roots, and all nonzero complex numbers have three distinct complex cube roots. For example, the real cube root of 8 is 2, because 2³ = 8.                                                                                                       (Source: Wikipedia)

Example to solve for cube root:

Let us see some of the example for solve for cube root for better understanding,
Example 1: solve for cube root `(^3sqrt (512))`
Solution:
Given: `(^3sqrt (512))`
Here, 512 is obtained by multiplying 8 three times. That is,
512 = 8 * 8 * 8`
(^3sqrt (512))` ` =` `(^3sqrt (8))`
= 8 `
Answer: solve for cube root `(^3sqrt (512)) = 8`

Example 2: solve for cube root` (^3sqrt (10^2 * 10^7))`
Solution:
Given: `(^3sqrt (10^2 * 10^7))`
(10^2 * 10^7) = (10 * 10) * (10 * 10 * 10 * 10 * 10 * 10 * 10)`
= (10 * 10 * 10) * (10 * 10 * 10) * (10 * 10 * 10) `
= 10^3 * 10^3 * 10^3 `
(^3sqrt (10^2 * 10^7)) = (^3sqrt (10 ^3* 10^3 * 10^3)) `
= 10 * 10 * 10 `
= 1000`
 Answer to solve for cube root:  `(^3sqrt (10 * 10 * 10)) = 1000`

Example 3: solve for cube root` (^3sqrt (17^2 * 17^4))`
Solution:
Given: `(^3sqrt (17^2 * 17^4))`
(17^2 * 17^4) = (17 * 17) * (17 * 17 * 17 * 17)`
= (17 * 17 * 17) * (17 * 17 * 17)`
= 17^3 * 17^3 * 17^3 `
(^3sqrt (17^2 * 17^4)) = (^3sqrt (17^3 * 17^3 * 17^3)) `
= 17 * 17 * 17 `
= 4913`
Answer to solve for cube root:  `(^3sqrt (17 * 17 * 17)) = 4913`

Example 4: solve for cube root  ` (^3sqrt (1/729))`
Solution:
Given: `(^3sqrt (1/729))`
1/729 = 1/8 * 1/8 * 1/8`
(^3sqrt (1/729)) = (^3sqrt (1/8^3))`
= 1/8 `
Answer: solve for cube root  `(^3sqrt (729)) = 1/8`

Example 5: solve for cube root  `(^3sqrt (1/8))`
Solution:
Given:  `(^3sqrt (1/8))`
1/8 = 1/2 * 1/2 * 1/2`
(^3sqrt (1/8)) = (^3sqrt (1/2^3))`
= 1/2 `
 Answer: solve for cube root  `(^3sqrt (1/8)) = 1/2`

Example 6: solve for cube root `(^3sqrt (343))`
Solution:
Given: `(^3sqrt (343))`
Here, 512 is obtained by multiplying 8 three times. That is,
343 = 7 * 7 * 7`
(^3sqrt (343))` ` =` `(^3sqrt (7^3))`
= 7 `
Answer: solve cube root `(^3sqrt (343)) = 7`

I am planning to write more post on Trig Reference Angles and tamil nadu samacheer kalvi 10th books. Keep checking my blog.

Practice problem for solve for cube root:

Practice problem for solve for cube root 1: `(^3sqrt (125))`
Answer: `(^3sqrt (125)) = 5`

Practice problem for solve for cube root 2: `(^3sqrt (216))`
Answer:` ( ^3sqrt (216)) = 6`

Practice problem for solve for cube root 3: `(^3sqrt (1331))`
Answer: `(^3sqrt (1331)) = 11`

Practice problem for solve for cube root 4:` (^3sqrt (1728))`
Answer: `(^3sqrt (1728)) = 12`

Practice problem for solve for cube root 5: `(^3sqrt (3375))`
Answer: `(^3sqrt (3375)) = 15`

Practice problem for solve for cube root 6: `(^3sqrt (27))`

Answer: `(^3sqrt (27)) = 9`