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Last updated on December 2nd, 2024
Cube root is defined as a value which when cubed gives the original number or it can be said as the value of βyβ where Itself multiplied thrice (yxyxy) equals 343. Cube roots find their uses in a wide range in our everyday activities including engineering, measuring densities and volumes of different shapes or designing open spaces.
We know that 343 is a perfect cube so the cube root of 343 is equal to 7. The cube root of 343 is written as β343, where the sign “β” denotes the radical.
We can find the cube root of 343, mainly through two methods:
i) Prime Factorization method.
ii) Subtraction method
To find a cube root of 343 the Prime Factorization method is one of the most widely and easiest methods to find the cube root of 343 that involves determining the factor of 343.
Step 1 — Find the prime factors of 343.
So, the prime factors of 343 are 7×7×7
Step 2 — The next thing you need to do is group the factors of 343 together in a group of 3(i.e., power of 3).
Step 3 — Here, we get the factor 7 in the power of 3, i.e., 73 or 7×7×7
The cube root of 343 can be written as β343 = β7×7×7 = 7
So through the above calculations, we can say that the cube root of 343 is 7.
This method involves subtracting successive odd numbers repeatedly. The list of odd numbers that should be subtracted successively are → 1,7,19,37,61,91,127,169,217,331,397 … This iteration will continue till we get a zero.
Step 1 — Subtract the 1st odd number : 343–1 = 342
Step 2 — Subtract the next odd number: 342–7 = 335
Step 3 — Subtract the next odd number: 335–19 = 316
Step 4 — Subtract the next odd number: 316–37 = 279
Step 5 — Subtract the next odd number: 279–61 = 218
Step 6 — Subtract the next odd number: 218– 91 = 127
Step 7 — Subtract the next odd number: 127–127 = 00
Here, the subtraction took place seven times to reach zero.
So from the above steps and calculations, the cube root of 343 is 7.