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Let's simplify the given expressions:

(a) (5+√3)(3+√2)

Expanding using the distributive property:

= 5 * 3 + 5 * √2 + √3 * 3 + √3 * √2

= 15 + 5√2 + 3√3 + √6

(b) (√5+√3)^2

Expanding using the formula (a+b)^2 = a^2 + 2ab + b^2:

= (√5)^2 + 2(√5)(√3) + (√3)^2

= 5 + 2√15 + 3

= 8 + 2√15

(c) (√7-√2)^2

Expanding using the formula (a-b)^2 = a^2 - 2ab + b^2:

= (√7)^2 - 2(√7)(√2) + (√2)^2

= 7 - 2√14 + 2

= 9 - 2√14

(d) (√7+√5)(√7-√5)

Using the formula (a-b)(a+b) = a^2 - b^2:

= (√7)^2 - (√5)^2

= 7 - 5

= 2

Simplified answers:

(a) 15 + 5√2 + 3√3 + √6

(b) 8 + 2√15

(c) 9 - 2√14

(d) 2

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