Need help with some questions:

1) Expand and simplify:

a)
[tex] \sqrt{5} ( \sqrt{6} + \sqrt{12} )[/tex]
b)
[tex](2 \sqrt{2} - 1)( \sqrt{6} + 2)[/tex]

2) Simplify fully, expressing each answer with a rational denominator:

i.
[tex] \frac{2}{ \sqrt{2} + \sqrt{8} } + \frac{1}{3} [/tex]
ii.
[tex] \frac{2}{3 - \sqrt{2} } + \frac{3}{2 \sqrt{3} + \sqrt{5} } [/tex]

3) Solve simultaneously for x and y given the equations:

[tex]3 {x}^{2} - 2y = 2 \: and \: 2x {}^{2} + 3y = 10[/tex]


4) The sum of 2 numbers is 23 and the product is 112.

i. Write down a pair of simultaneous equations to represent the information.

ii. Find the two numbers
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