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Find the Cube Root of the Following Natural Number 74088000 . - Mathematics

Sum

Find the cube root of the following natural number 74088000 .

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Solution

Cube root by factors:
On factorising 74088000 into prime factors, we get:

\[74088000 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 5 \times 5 \times 5 \times 7 \times 7 \times 7\
On grouping the factors in triples of equal factors, we get:
\[74088000 = \left\{ 2 \times 2 \times 2 \right\} \times \left\{ 2 \times 2 \times 2 \right\} \times \left\{ 3 \times 3 \times 3 \right\} \times \left\{ 5 \times 5 \times 5 \right\} \times \left\{ 7 \times 7 \times 7 \right\}\]
Now, taking one factor from each triple, we get:
\[\sqrt[3]{74088000} = 2 \times 2 \times 3 \times 5 \times 7 = 420\]

 

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APPEARS IN

RD Sharma Class 8 Maths
Chapter 4 Cubes and Cube Roots
Exercise 4.3 | Q 4.09 | Page 22
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