Question

548^2-420^2 и все это в √ 

Answer 1

√548²-420²=548-420=128 (корень и квадраты как бы компенсируются)

Answer 2

To simplify the expression √(548^2-420^2), we can use the difference of squares identity:

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

Let's apply this identity with a = 548 and b = 420:

548^2 - 420^2 = (548 + 420)(548 - 420) = 968 * 128

Now we can substitute this back into the original expression:

√(548^2-420^2) = √(968 * 128) = √(8^3 * 11 * 2^7)

We can simplify this expression by taking out the perfect square factors:

√(8^3 * 11 * 2^7) = √(2^6 * 4 * 11 * 2^1 * 2^1 * 2^1) = 2^3 * √(11 * 2^3) = 8√(88)

Therefore, √(548^2-420^2) simplifies to 8√88.