Tính giá trị biểu thức

To simplify the expressions M and N, we can use the formula for the difference of squares:

a^2 - b^2 = (a + b)(a - b)

For M:
M = √(9 + 4√5) - √(9 - 4√5)

Let's simplify the expression inside the square roots first:
(9 + 4√5) - (9 - 4√5)
= 9 + 4√5 - 9 + 4√5
= 8√5

Now we can rewrite M:
M = √(8√5)

To simplify this further, we can rewrite it as a product of square roots:
M = √(4 * 2√5)
= √4 * √(2√5)
= 2 * √(2√5)
= 2√(2√5)

For N:
N = √(8 - 2√7) - √(8 + 2√7)

Let's simplify the expression inside the square roots first:
(8 - 2√7) - (8 + 2√7)
= 8 - 2√7 - 8 - 2√7
= -4√7

Now we can rewrite N:
N = √(-4√7)

Since the expression inside the square root is negative, N is not a real number.