PUMPA - SMART LEARNING
எங்கள் ஆசிரியர்களுடன் 1-ஆன்-1 ஆலோசனை நேரத்தைப் பெறுங்கள். டாப்பர் ஆவதற்கு நாங்கள் பயிற்சி அளிப்போம்
Book Free DemoSteps to find the cube root of a number through prime factorisation:
Step 1: Find the prime factorisation of the given number.
Step 2: Group the factors in pair of three numbers (triplet).
Step 3: If there are no factor leftover, then the given number is a perfect cube. Otherwise, it is not a perfect cube.
Step 4: Now, take one factor common from each pair and multiply them.
Step 5: The obtained product is a cube root of a given number.
Example:
1. Find the value of \(\sqrt[3]{216}\).
Solution:
Let us first find the prime factor of \(216\).
Group the factors in pair of three numbers.
\(216 = (2 \times 2 \times 2) \times (3 \times 3 \times 3)\)
Here, no factor is leftover. Therefore, \(216\) is a perfect cube.
Now, take one factor common from each pair and multiply them.
\(\sqrt[3]{216} = 2 \times 3 = 6\)
Therefore, the value of \(\sqrt[3]{216} = 6\).
2. Evaluate the value of .
Solution:
The given number is .
Let us first factorise the numbers \(2197\) and \(1000\).
\(=\)
\(=\)
\(=\)
\(=\) (Cube and cube root get cancelled)
Therefore, the value of \(=\) .