Answer:

Step-by-step explanation:
<u>Ratios
</u>
We are given the following relations:
![a=\sqrt{7}+\sqrt{c}\qquad \qquad[1]](https://tex.z-dn.net/?f=a%3D%5Csqrt%7B7%7D%2B%5Csqrt%7Bc%7D%5Cqquad%20%5Cqquad%5B1%5D)
![b=\sqrt{63}+\sqrt{d}\qquad \qquad[2]](https://tex.z-dn.net/?f=b%3D%5Csqrt%7B63%7D%2B%5Csqrt%7Bd%7D%5Cqquad%20%5Cqquad%5B2%5D)
![\displaystyle \frac{c}{d}=\frac{1}{9} \qquad \qquad [3]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bc%7D%7Bd%7D%3D%5Cfrac%7B1%7D%7B9%7D%20%5Cqquad%20%5Cqquad%20%5B3%5D)
From [3]:

Replacing into [2]:

We can express 63=9*7:

Taking the square root of 9:

Factoring:

Find the ration a:b:

Simplifying:

Answer:
i)16
ii)9
Step-by-step explanation:
![\sqrt{256} \\=\sqrt{16*16} \\=16\\\\ii)\ \sqrt[3]{729}\\ =\sqrt[3]{9*9*9} \\=9](https://tex.z-dn.net/?f=%5Csqrt%7B256%7D%20%5C%5C%3D%5Csqrt%7B16%2A16%7D%20%5C%5C%3D16%5C%5C%5C%5Cii%29%5C%20%5Csqrt%5B3%5D%7B729%7D%5C%5C%20%3D%5Csqrt%5B3%5D%7B9%2A9%2A9%7D%20%5C%5C%3D9)