Question

Find the value of ✓-5 X ✓-10 X ✓-10​

Answer 1

$\large\underline{\underline{Question:}}$

$\underline{Find\:the\:value\:of:}$

$\sqrt{-5} × \sqrt{-10} × \sqrt{-10}$

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$\large\underline{\underline{To\:Find:}}$

The value of the Equation..

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$\large\underline{\underline{we\:know:}}$

$\sqrt{-5} = \infty\:or\:undefined$

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$\large\underline{\underline{Solution:}}$

$\sqrt{\infty} × \sqrt{-10} × \sqrt{-10}$

$\Rightarrow \sqrt{\infty} × \sqrt{-10} × \sqrt{-10}$

$\Rightarrow \sqrt{\infty × -10 × -10}$

$\Rightarrow \infty$

Answer 2

Answer:

$\sf{The \ value \ of \ \sqrt-5\times\sqrt-10\times\sqrt-5}$

$\sf{is \ -10\sqrt{5}i.}$

To find:

• $\sf{The \ value \ of \ \sqrt-5\times\sqrt-10\times\sqrt-5}$

Solution:

$\sf{\leadsto{\sqrt{-5}\times\sqrt{-10}\times\sqrt{-10}}}$

$\sf{We \ know, \sqrt-1=i}$

$\sf{\leadsto{\sqrt5(i)\times\sqrt10(i)\times\sqrt10(i)}}$

$\sf{\leadsto{10\sqrt5(i)^{3}}}$

$\sf{But, \ i^{3}=-i}$

$\sf{\leadsto{-10\sqrt{5}i}}$

$\sf\purple{\tt{\therefore{The \ value \ of \ \sqrt-5\times\sqrt-10\times\sqrt-5}}}$

$\sf\purple{\tt{is \ -10\sqrt{5}i.}}$