Question

(√(√8-3)^2)-(√(√2-3)^2)

Answer 1

Ответ:

Объяснение:

√(√8-3)^2)-(√(√2-3)^2=√8-3-√2+3=2√2-√2=√2

Answer 2

Let's simplify the expression step by step:

1. (√(√8 - 3)^2) = (√(2√2 - 3)^2) [since √8 = √(222) = √(2√2)] = (√(2√2 - 3))^2 [by squaring both sides] = (2√2 - 3)^2 [by removing the square root]

2. (√(√2 - 3)^2) = (√(2^(1/4) - 3)^2) [since √2 = 2^(1/2) and √8 = 2^(3/2)] = (√(2^(1/4) - 3))^2 [by squaring both sides] = (2^(1/4) - 3)^2 [by removing the square root]

Now, let's substitute these values back into the original expression:

(√(√8 - 3)^2) - (√(√2 - 3)^2) = (2√2 - 3)^2 - (2^(1/4) - 3)^2

Now, we have two squared terms, so we can use the formula (a^2 - b^2) = (a + b)(a - b):

= [(2√2 - 3) + (2^(1/4) - 3)][(2√2 - 3) - (2^(1/4) - 3)]

Now, simplify further:

= (2√2 - 2^(1/4))(2√2 - 2^(1/4))

Now, let's multiply these two terms:

= 4 * (√2) * 2^(1/4) - 2^(1/4) * 2√2 - 2^(1/4) * 2√2 + 2^(1/4) * 2^(1/4)

Since 2^(1/4) is the fourth root of 2, we can rewrite it as √(√2):

= 4 * (√2) * √(√2) - 2^(1/4) * 2√2 - 2^(1/4) * 2√2 + √2

Now, simplify further:

= 4 * √(2 * 2) - 2^(1/4) * 2√2 - 2^(1/4) * 2√2 + √2 = 4 * 2 - 2^(1/4) * 2√2 - 2^(1/4) * 2√2 + √2 = 8 - 4 * 2^(5/4) + √2

So, the simplified expression is 8 - 4 * 2^(5/4) + √2.