Show That: 3 √ − 125 − 1000 = 3 √ − 125 × 3 √ − 1000 - Mathematics

Sum

Show that:\[\sqrt[3]{- 125 - 1000} = \sqrt[3]{- 125} \times \sqrt[3]{- 1000}\]

Solution

LHS = \[\sqrt[3]{- 125 \times - 1000} = \sqrt[3]{- 5 \times - 5 \times - 5 \times - 10 \times - 10 \times - 10} = \sqrt[3]{\left\{ - 5 \times - 5 \times - 5 \right\} \times \left\{ - 10 \times - 10 \times - 10 \right\}} = - 5 \times - 10 = 50\]

RHS = \[\sqrt[3]{- 125} \times \sqrt[3]{- 1000} = \sqrt[3]{- 5 \times - 5 \times - 5} \times \sqrt[3]{\left\{ - 10 \times - 10 \times - 10 \right\}} = - 5 \times - 10 = 50\]

Because LHS is equal to RHS, the equation is true.

Concept: Concept of Cube Root

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Chapter 4: Cubes and Cube Roots - Exercise 4.4 [Page 30]

Q 2.4 Q 2.3 Q 3.1

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