Hello: ) i’m not sure how to factorise the square root, anyone able to explain & also check my answer? !

You're on the right track, but you made an error when you wrote out

4a+15 = -7

Instead it should be

-(4a+15) = -7

which is the same as

4a+15 = 7

This is because the  "-(4a+15)*sqrt(3)" and "-7sqrt(3)" terms both start with a negative. Solving 4a+15 = 7 leads to a = -2

Use a = -2 and you should get b = 2

Check:

Plug in a = -2 into the LHS and compute

(4-3*sqrt(3))*(5-a*sqrt(3)) = (4-3*sqrt(3))*(5+2*sqrt(3)) = -10.1243556529821

plug b = 2 into the RHS and compute

b - 7*sqrt(3) = 2 - 7*sqrt(3) = -10.1243556529821

we get the same approximate value on each side, so LHS = RHS when a = -2 and b = 2.

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step-by-step explanation: