Math, asked by jannat627477, 1 year ago

value of √343×√-27is ​

Answers

Answered by sam43656
1

-21root 21 is your answer

Answered by AbhijithPrakash
8

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

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