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lisov135 [29]
3 years ago
14

Which expression is equivalent to √4j^4/9k^8?

Mathematics
2 answers:
solmaris [256]3 years ago
6 0
\frac{ 2j^{2} }{ 3^{4} }
SQRT each individual bit: 4 andj^{4} and 9 and k^{8}
umka2103 [35]3 years ago
4 0

Answer:

Option (4) is correct.

An equivalent expression to the given expression   \sqrt{\frac{4j^4}{9k^8}} is \frac{2j^2}{3k^4}

Step-by-step explanation:

Given expression  \sqrt{\frac{4j^4}{9k^8}}

We have to choose an equivalent expression to the given expression   \sqrt{\frac{4j^4}{9k^8}}

Consider the given expression  \sqrt{\frac{4j^4}{9k^8}}

Apply radical rule,

\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}

=\frac{\sqrt{4}\sqrt{j^4}}{\sqrt{9}\sqrt{k^8}}

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

\sqrt{4j^4}=\sqrt{4}\sqrt{j^4}

\sqrt{9k^8}=\sqrt{9}\sqrt{k^8}

We have,

=\frac{\sqrt{4}\sqrt{j^4}}{\sqrt{9}\sqrt{k^8}}

=\frac{2\sqrt{j^4}}{3\sqrt{k^8}}

\mathrm{Apply\:radical\:rule\:}\sqrt[n]{a^m}=a^{\frac{m}{n}}

=\frac{2j^2}{3k^4}

Thus, An equivalent expression to the given expression   \sqrt{\frac{4j^4}{9k^8}} is \frac{2j^2}{3k^4}

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