![\sqrt[]{5}](https://img.qammunity.org/2023/formulas/mathematics/college/bp1djlgqnawyaicjz3vzvap72y230s3bg2.png)
As 5 is a prime number, it is not in the power of 2. Then, the expression cannot be simplified,
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![\sqrt[3]{8}](https://img.qammunity.org/2023/formulas/mathematics/high-school/ofc70nsmyulwvbt3gansykub0txjitnd4n.png)
Prime factorization of 8 is:

Then, the expression can be simplified to get;
![\sqrt[3]{8}=\sqrt[3]{2^3}=2](https://img.qammunity.org/2023/formulas/mathematics/college/3ckg36ffqhera7rqalsq42eluqzeihl6rz.png)
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![\sqrt[]{3+5}](https://img.qammunity.org/2023/formulas/mathematics/college/mec6exgt409lue6b14glbgal8zmzd5w8ou.png)
To simplify the expression first add numbers, and then use the prime factorization of result as follow:
![=\sqrt[]{8}=\sqrt[]{2^3}=\sqrt[]{2^2*2}=2\sqrt[]{2}](https://img.qammunity.org/2023/formulas/mathematics/college/16w4imcvz6clbwnks5l1p5r9qnx2va1bp0.png)
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![\sqrt[\square]{(2x)/(3y)}](https://img.qammunity.org/2023/formulas/mathematics/college/988vkvqyy9drkz0rosb5gidfps30mhl5gh.png)
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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Use the next property to rewrite the expression:
![a^(n/m)=\sqrt[m]{a^n}](https://img.qammunity.org/2023/formulas/mathematics/college/z0t5qods3vpdr9kx4i83ec3v7bj24k2zmc.png)
![(x^4y)^(2/3)=\sqrt[3]{(x^4y)^2}](https://img.qammunity.org/2023/formulas/mathematics/college/hvrbbljqh6ic3n96gvqvbfd2lyd8f6y0tq.png)
Expand the expression under the root and then simplifiy the expression as follow:
![=\sqrt[3]{x^8y^2}=\sqrt[3]{x^6^{}x^2y^2}=x^2\sqrt[3]{x^2y^2}](https://img.qammunity.org/2023/formulas/mathematics/college/i54x8e1mihemyham5pmoekw83ms83gyy5z.png)