Question

Evaluate :$3\sqrt{(-729)*2197}$

Answer 1

Explanation:

We wish to simplify and evaluate the answer for $\mathsf{\sqrt[3]{(-729)\times2197}}$.

First, let us factorize each of the terms, i.e., -729 and 2197.

$\mathsf{-729=-(3\times3\times3\times3\times3\times3)=-(9\times9\times9)=(-9)\times(-9)\times(-9)}$

$\mathsf{2197=13\times13\times13}$

We know that we can write $\sqrt[n]{a\times b}$ as $\mathsf{\sqrt[n]{a}\times \sqrt[n]{b} }$ where n can be any natural number.

∴ $\mathsf{\sqrt[3]{(-729) \times 2197}}$

$\mathsf{=\sqrt[3]{-729}\times\sqrt[3]{2197}}$

$\mathsf{=\sqrt[3]{(-9)\times(-9)\times(-9)} \times \sqrt[3]{13\times13\times13}}}$

$\mathsf{=(-9)\times13 = -117}$

Answer: -117

I hope this helps. :D