Answer:
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Step-by-step explanation:
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Answer:
![\sqrt[3]{2y^3} * 7\sqrt{18y} = 21(y^{\frac{3}{2}})(2^{\frac{5}{6}})](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B2y%5E3%7D%20%2A%207%5Csqrt%7B18y%7D%20%3D%2021%28y%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%29%282%5E%7B%5Cfrac%7B5%7D%7B6%7D%7D%29)
Step-by-step explanation:
The question is poorly formatted.
Given
![\sqrt[3]{2y^3} * 7\sqrt{18y}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B2y%5E3%7D%20%2A%207%5Csqrt%7B18y%7D)
Required
Derive an equivalent expression
![\sqrt[3]{2y^3} * 7\sqrt{18y}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B2y%5E3%7D%20%2A%207%5Csqrt%7B18y%7D)
Express 18 as 9 * 2
![\sqrt[3]{2y^3} * 7\sqrt{9 * 2y}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B2y%5E3%7D%20%2A%207%5Csqrt%7B9%20%2A%202y%7D)
Split the expression as follows:
![\sqrt[3]{2y^3} * 7\sqrt{9} * \sqrt{2y}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B2y%5E3%7D%20%2A%207%5Csqrt%7B9%7D%20%2A%20%5Csqrt%7B2y%7D)
Take positive square root of 9
![\sqrt[3]{2y^3} * 7*3 * \sqrt{2y}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B2y%5E3%7D%20%2A%207%2A3%20%2A%20%5Csqrt%7B2y%7D)
![\sqrt[3]{2y^3} * 21 * \sqrt{2y}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B2y%5E3%7D%20%2A%2021%20%2A%20%5Csqrt%7B2y%7D)
![21*\sqrt[3]{2y^3} * \sqrt{2y}](https://tex.z-dn.net/?f=21%2A%5Csqrt%5B3%5D%7B2y%5E3%7D%20%2A%20%20%5Csqrt%7B2y%7D)
The cube root can be rewritten to give:
![21*\sqrt[3]{2}*\sqrt[3]{y^3} * \sqrt{2y}](https://tex.z-dn.net/?f=21%2A%5Csqrt%5B3%5D%7B2%7D%2A%5Csqrt%5B3%5D%7By%5E3%7D%20%2A%20%20%5Csqrt%7B2y%7D)
![\sqrt[3]{y^3} = y^{3*\frac{1}{3}} = y](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7By%5E3%7D%20%3D%20y%5E%7B3%2A%5Cfrac%7B1%7D%7B3%7D%7D%20%3D%20y)
So, we have:
![21*\sqrt[3]{2} * y * \sqrt{2y}](https://tex.z-dn.net/?f=21%2A%5Csqrt%5B3%5D%7B2%7D%20%2A%20y%20%2A%20%20%5Csqrt%7B2y%7D)
Rewrite as:
![21y *\sqrt[3]{2} * \sqrt{2y}](https://tex.z-dn.net/?f=21y%20%2A%5Csqrt%5B3%5D%7B2%7D%20%20%2A%20%20%5Csqrt%7B2y%7D)
Split 
![21y *\sqrt[3]{2} * \sqrt{2} * \sqrt{y}](https://tex.z-dn.net/?f=21y%20%2A%5Csqrt%5B3%5D%7B2%7D%20%20%2A%20%20%5Csqrt%7B2%7D%20%2A%20%5Csqrt%7By%7D)
Collect Like Terms
![21y*\sqrt{y} *\sqrt[3]{2} * \sqrt{2}](https://tex.z-dn.net/?f=21y%2A%5Csqrt%7By%7D%20%2A%5Csqrt%5B3%5D%7B2%7D%20%20%2A%20%20%5Csqrt%7B2%7D)
Represent in index form

Apply law of indices




Hence:
![\sqrt[3]{2y^3} * 7\sqrt{18y} = 21(y^{\frac{3}{2}})(2^{\frac{5}{6}})](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B2y%5E3%7D%20%2A%207%5Csqrt%7B18y%7D%20%3D%2021%28y%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%29%282%5E%7B%5Cfrac%7B5%7D%7B6%7D%7D%29)
Answer:
0.875
Step-by-step explanation:
they're proportional.
Factor the numerator and denominator...
(n^4-5n^2-6n^2+30)/(n^4-2n^2-5n^2+10)
[n^2(n^2-5)-6(n^2-5)]/[n^2(n^2-2)-5(n^2-2)]
[(n^2-5)(n^2-6)]/[(n^2-5)(n^2-2)] notice the (n^2-5)s cancel out
(n^2-6)/(n^2-2)
We could further factor this because each is a difference of squares to:
[(n+√6)(n-√6)]/[(n+√2)(n-√2)