Question

value of √343×√-27is ​

Answer 1

-21root 21 is your answer

Answer 2

Answer:

$\green{\sqrt{343}\sqrt{-27}=21\sqrt{21}i}$

Step-by-step explanation:

$\sqrt{343}\sqrt{-27}$

$\black{\sqrt{343}}$

$\gray{\mathrm{Prime\:factorization\:of\:}343:\quad 7^3}$

$=\sqrt{7^3}$

$\gray{\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^b\times \:a^c}$

$=\sqrt{7^2\times \:7}$

$\gray{\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}}$

$=\sqrt{7^2\times \:7}$

$\gray{\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}}$

$=\sqrt{7}\sqrt{7^2}$

$\gray{\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{a^n}=a}$

$\gray{\sqrt{7^2}=7}$

$=7\sqrt{7}$

$=7\sqrt{7}\sqrt{-27}$

$\black{\sqrt{-27}}$

$\gray{\mathrm{Apply\:radical\:rule}:\quad \sqrt{-a}=\sqrt{-1}\sqrt{a}}$

$\gray{\sqrt{-27}=\sqrt{-1}\sqrt{27}}$

$=\sqrt{-1}\sqrt{27}$

$\gray{\mathrm{Apply\:imaginary\:number\:rule}:\quad \sqrt{-1}=i}$

$=\sqrt{27}i$

$\gray{\sqrt{27}=3\sqrt{3}}$

$=3\sqrt{3}i$

$=7\times \:3\sqrt{7}\sqrt{3}i$

$\gray{\mathrm{Multiply\:the\:numbers:}\:7\times \:3=21}$

$=21\sqrt{7}\sqrt{3}i$

$\gray{\mathrm{Apply\:radical\:rule}:\quad \sqrt{a}\sqrt{b}=\sqrt{ab}}$

$\gray{\sqrt{7}\sqrt{3}=\sqrt{7\times \:3}}$

$=21i\sqrt{7\times \:3}$

$\gray{\mathrm{Multiply\:the\:numbers:}\:7\times \:3=21}$

$=21\sqrt{21}i$