Multiply (519 −−−√ ) (62–√). Give an exact answer

Answer 1

To solve this equation, we need to simplify the given expressions inside the square roots.

Given: (519 - √(x))(62 - √(y))

Now, let's simplify the square roots:

√(x) = √(519) = √(3 * 173)

Since 173 is a prime number, we can't simplify it further. Hence,

√(x) = √(3 * 173) = √(3) * √(173) = √(3)√(173)

Similarly,

√(y) = √(62) = √(2 * 31)

Since 2 and 31 are both prime numbers, we can't simplify them further. Hence,

√(y) = √(2 * 31) = √(2) * √(31) = √(2)√(31)

Now, the equation becomes:

(519 - √(3)√(173))(62 - √(2)√(31))

To find the exact answer, we need to multiply the terms:

= 519 * 62 - 519 * √(2)√(31) - √(3)√(173) * 62 + √(3)√(173) * √(2)√(31)

= 32178 - 519√(2)√(31) - 62√(3)√(173) + 519√(3)√(2)√(31)√(173)

Since square roots can only be simplified if both numbers under the root sign are the same, we conclude that we've reached the most simplified form of the equation. Hence, the exact answer is:

32178 - 519√(2)√(31) - 62√(3)√(173) + 519√(3)√(2)√(31)√(173)