The correct option is C 12|ba| Here, √(36a^4b^6144a^6b^4) = √(36b^2144a^2) = 612√( (ba)^2) = 12|ba| ...

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Laws of Exponents

√36a4b6144a6b...

Question

$\sqrt{\frac{36 a^{4} b^{6}}{144 a^{6} b^{4}}}$ = ?

∣ ∣ ∣ \frac{1}{2} \frac{b}{a} ∣ ∣ ∣

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2 ∣ ∣ ∣ \frac{b}{a} ∣ ∣ ∣

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\frac{1}{2} ∣ ∣ ∣ \frac{b}{a} ∣ ∣ ∣

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\frac{3}{2} ∣ ∣ ∣ \frac{b}{a} ∣ ∣ ∣

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Solution

The correct option is C $\frac{1}{2} ∣ ∣ ∣ \frac{b}{a} ∣ ∣ ∣$
Here, $\sqrt{\frac{36 a^{4} b^{6}}{144 a^{6} b^{4}}}$

$=$ $\sqrt{\frac{36 b^{2}}{144 a^{2}}}$

$=$ $\frac{6}{12} \sqrt{{(\frac{b}{a})}^{2}}$

$=$ $\frac{1}{2} ∣ ∣ ∣ \frac{b}{a} ∣ ∣ ∣$

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