[tex]\sqrt[]{5}[/tex]
As 5 is a prime number, it is not in the power of 2. Then, the expression cannot be simplified,
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[tex]\sqrt[3]{8}[/tex]
Prime factorization of 8 is:
[tex]\begin{gathered} 8=2\times2\times2 \\ 8=2^3 \end{gathered}[/tex]
Then, the expression can be simplified to get;
[tex]\sqrt[3]{8}=\sqrt[3]{2^3}=2[/tex]
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[tex]\sqrt[]{3+5}[/tex]
To simplify the expression first add numbers, and then use the prime factorization of result as follow:
[tex]=\sqrt[]{8}=\sqrt[]{2^3}=\sqrt[]{2^2\times2}=2\sqrt[]{2}[/tex]
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[tex]\sqrt[\square]{\frac{2x}{3y}}[/tex]
As both parts of the fraction under the root are not power of two and both are prime numbers the expression cannot be simplified.
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[tex](x^4y)^{2/3}[/tex]
Use the next property to rewrite the expression:
[tex]a^{n/m}=\sqrt[m]{a^n}[/tex][tex](x^4y)^{2/3}=\sqrt[3]{(x^4y)^2}[/tex]
Expand the expression under the root and then simplifiy the expression as follow:
[tex]=\sqrt[3]{x^8y^2}=\sqrt[3]{x^6^{}x^2y^2}=x^2\sqrt[3]{x^2y^2}[/tex]
