Answer:
a. 
b. 
c. 
d. 
e. 
Step-by-step explanation:
a.
![\sqrt{12} - \sqrt{108} - \sqrt[3]{27}](https://tex.z-dn.net/?f=%5Csqrt%7B12%7D%20-%20%5Csqrt%7B108%7D%20-%20%5Csqrt%5B3%5D%7B27%7D)
Expand each expression
![\sqrt{4*3} - \sqrt{36 * 3} - \sqrt[3]{3*3*3}](https://tex.z-dn.net/?f=%5Csqrt%7B4%2A3%7D%20-%20%5Csqrt%7B36%20%2A%203%7D%20-%20%5Csqrt%5B3%5D%7B3%2A3%2A3%7D)
Split the first two surds
![\sqrt{4}*\sqrt{3} - \sqrt{36} * \sqrt{3} - \sqrt[3]{3*3*3}](https://tex.z-dn.net/?f=%5Csqrt%7B4%7D%2A%5Csqrt%7B3%7D%20-%20%5Csqrt%7B36%7D%20%2A%20%5Csqrt%7B3%7D%20-%20%5Csqrt%5B3%5D%7B3%2A3%2A3%7D)
![2*\sqrt{3} - 6 * \sqrt{3} - \sqrt[3]{3*3*3}](https://tex.z-dn.net/?f=2%2A%5Csqrt%7B3%7D%20-%206%20%2A%20%5Csqrt%7B3%7D%20-%20%5Csqrt%5B3%5D%7B3%2A3%2A3%7D)
Apply law of indices
![2*\sqrt{3} - 6 * \sqrt{3} - \sqrt[3]{3^3}](https://tex.z-dn.net/?f=2%2A%5Csqrt%7B3%7D%20-%206%20%2A%20%5Csqrt%7B3%7D%20-%20%5Csqrt%5B3%5D%7B3%5E3%7D)
Apply law of indices





Factorize

<em>The expression cannot be further simplified</em>
b.

Expand the expression

Apply the following law of indices;



Add the exponents



<em>The expression cannot be further simplified</em>
c.

Rationalize the denominator


Simplify the numerator

Simplify the denominator by difference of two squares


<em>The expression cannot be further simplified</em>
<em></em>
d.

Expand the expression

Open the bracket

Open both brackets


Multiply each expression in the bracket


Solve like terms

Take square root of 25 and y²


Remove the brackets

<em>The expression cannot be further simplified</em>
e.

This expression can not be simplified; However, it can be rewritten, by applying law of indices as
