Question

by what smallest natural number should -6125 be multiplied so that the product becomes a perfect cube??​

Answer 1

$\huge\underline\bold\red{Answer}$:

If we put all of it together we have the factors 5 x 5 x 5 x 7 x 7 = 6,125. It can also be written in exponential form as 5³x 7² $\mathcal\purple{IT SHOULD BE MULTIPLY BY 7}$so the product obtained will be 42875 and it is a perfect cube

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Answer 2

${\huge{\underline{\boxed{\red{\mathcal{Answer}}}}}}$

$\\ \text{Prime factors of -6125 \longrightarrow }\\ \Large{ \begin{array}{c|c} \tt 5 & \sf{-6125} \\ \cline{1-2} \tt 5 & \sf {-1225} \\ \cline{1-2} \tt 5 & \sf{-245} \\ \cline{1-2} \tt 7 & \sf{-49}\\ \cline{1-2} \tt 7 & \sf{-7}\\ \cline{1-2} \tt -1 & \sf{-1} \\ \cline{1-2} & \sf{1} \end{array}} \\ \\ \implies -6125 = 5*5*5*7*7*(-1) \\\implies -6125 = (-5)^3 * 7^2 \:\:\:\:\:\:OR\:\:\:\:\:\: -6125 = 5^3 * (-7)^2$

So, the number which when multiplied by (-6125) becomes a perfect cube, will be either 7[if we take (-5)] or -7[if we take +5]. But we need to take a natural number,hence the number will be 7.

The product obtained will be -42875, which is the perfect cube of -35

Hope it helps!!!