Question

(√2-3√5)²+√360 решите пожалуйста

Answer 1

Ответ:

$\displaystyle \bf (\sqrt{2}-3\sqrt{5})^2+\sqrt{360}=47$

Объяснение:

Вычислить:

$\displaystyle \bf (\sqrt{2}-3\sqrt{5})^2+\sqrt{360}$

Квадрат разности двух чисел:

(a - b)² = a² - 2ab + b²

Свойства степеней:

√(ab) = √a · √b

$\displaystyle (\sqrt{2}-3\sqrt{5})^2+\sqrt{360}=(2-2\cdot\sqrt{2}\cdot3\sqrt{5} +9\cdot5) +\sqrt{36\cdot10} =\\\\=2-6\sqrt{2\cdot5}+45+\sqrt{36}\cdot\sqrt{10}=47-6\sqrt{10}+6\sqrt{10}=47$

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Answer 2

Sure, I'd be happy to help you solve the expression.

Let's first simplify the expression (√2 - 3√5)² + √360 step by step:

Step 1: Expand the square of the binomial (√2 - 3√5)² (√2 - 3√5)² = (√2 - 3√5)(√2 - 3√5) Using the formula (a - b)² = a² - 2ab + b²: (√2 - 3√5)² = (√2)² - 2(√2)(3√5) + (3√5)² = 2 - 2√10 + 9√5

Step 2: Simplify √360 √360 = √(36 * 10) = √36 * √10 = 6√10

Now, let's put it all together and solve the expression:

(√2 - 3√5)² + √360 = (2 - 2√10 + 9√5) + 6√10 Now, combine like terms: = 2 + 6√10 + 9√5 - 2√10 = 2 + (6√10 - 2√10) + 9√5 = 2 + 4√10 + 9√5

So, the simplified form of the expression is 2 + 4√10 + 9√5.