(5*sqrt3)^2 = 25*3 = 75
Its basically saying 5 multiplied by the square root of 3 and whatever you get from doing that, square.
Just find the square root of 3, if you can use a calculator, which comes out to approx. 1.732.... and multiply by 5, which comes to like 8.6602.... Then square that number, and you get 75. Done.
Please don't use a calculator - the problem certainly doesn't require one.
(5 * sqrt(3) ) ^2.
The exponent applies to both things inside the parentheses - in other words, the problem could be rewritten as 5^2 times (sqrt(3))^2.
5^2 = 25.
sqrt(3) ^ 2 = 3. (Taking the square root and squaring something are inverse operations, and cancel each other out, much like how addition and subtraction or multiplication and division are inverse operations.)
So now you have 25 * 3 = 75.
Another example:
(7 * sqrt(5) )^2 = 7^2 * (sqrt(5))^2 = 49 * 5 = 245.
No calculator required.