Question

Знайти значення виразу √(√41-√5)*√(√5+√41)

Answer 1

$\sqrt{\sqrt{41}-\sqrt5}\cdot \sqrt{\sqrt5+\sqrt{41}} =\sqrt{(\sqrt{41}-\sqrt5)(\sqrt{41}+\sqrt5)}=\\\\=\sqrt{(\sqrt{41})^2-(\sqrt5)^2}=\sqrt{41-5}=\sqrt{36}=6$

Answer 2

$\sqrt{( \sqrt{41} - \sqrt{5}) } \sqrt{( \sqrt{5} + \sqrt{41}) } = \sqrt{( \sqrt{41} - \sqrt{5} )( \sqrt{41} + \sqrt{5} )} = \sqrt{(41 - 5)} = \sqrt{36} = 5$

Answer 3

To evaluate the expression √(√41 - √5) * √(√5 + √41), follow these steps:

Step 1: Simplify the expressions within the square roots. Step 2: Perform the operations within the square roots. Step 3: Evaluate the entire expression.

Step 1: Simplify the expressions within the square roots. √41 = √(25 + 16) = √25 * √(1 + 16/25) = 5 * √(1.64)

√5 = √(4 + 1) = √4 * √(1 + 1/4) = 2 * √(1.25)

Step 2: Perform the operations within the square roots. √(√41 - √5) = √(5 * √(1.64) - 2 * √(1.25)) = √(5 * 1.28 - 2 * 1.12) = √(6.4 - 2.24) = √4.16 ≈ 2.04

√(√5 + √41) = √(2 * √(1.25) + 5 * √(1.64)) = √(2 * 1.12 + 5 * 1.28) = √(2.24 + 6.4) = √8.64 ≈ 2.94

Step 3: Evaluate the entire expression. √(√41 - √5) * √(√5 + √41) ≈ 2.04 * 2.94 ≈ 5.9952

So, the approximate value of the expression √(√41 - √5) * √(√5 + √41) is 5.9952.