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9514 1404 393

Answer:

47 -6√10

Explanation:

As you know, the area of a square is the square of the side length. It can be helpful here to make use of the form for the square of a binomial.

(a -b)² = a² - 2ab + b²

(√2 -3√5)² = (√2)² - 2(√2)(3√5) + (3√5)²

= 2 - 6√10 + 3²(5)

= 47 -6√10

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Check

√2-3√5 ≈ -5.29399 . . . . . . . . note that a negative value for side length makes no sense, so this isn't about geometry, it's about binomials and radicals

(√2-3√5)² ≈ 28.02633

47 -6√10 ≈ 28.02633

User Rohit Shedage
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