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Answer :
we have
[tex]\sqrt{54x^{9}y^{7}}[/tex]
we know that
[tex]54=2*3^{3} =2*3*3^{2}\\ x^{9}= x^{8}*x \\ y^{7}=y^{6}*y[/tex]
Substitute
[tex]\sqrt{(2*3*3^{2})*(x^{8}*x)*(y^{6}*y)}=[{(2*3*3^{2})*(x^{8}*x)*(y^{6}*y)}]^{\frac{1}{2}} \\ \\[/tex]
[tex]={(2*3*3^{2})^{\frac{1}{2}}*(x^{8}*x)^{\frac{1}{2}}*(y^{6}*y)}^{\frac{1}{2}}[/tex]
[tex]={(2*3)^{\frac{1}{2}}*(3^{2})^{\frac{1}{2}}*(x^{8})^{\frac{1}{2}}*(x)^{\frac{1}{2}}*(y^{6})^{\frac{1}{2}}*(y)}^{\frac{1}{2}}[/tex]
[tex]={(2*3*x*y)^{\frac{1}{2}}*(3)*(x^{4})*(y^{3})[/tex]
[tex]=3x^{4}y^{3}\sqrt{6xy}[/tex]
therefore
the answer is
[tex]3x^{4}y^{3}\sqrt{6xy}[/tex]
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Rewritten by : Barada
Simplify the square root of 54x^9y^7 or √(54x^9y^7)
54x^9y^7 = (3x^4y^3)^2 (6xy)
Now square root of (3x^4y^3)^2 = 3x^4y^3
So the final answer is 3x^4y^3 √(6xy)
Hence option “B” is correct.
