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

Question

An abstract image depicting the concept of mathematical operations and numbers. The image should contain symbols and representations of mathematical operations, such as multiplication and square root. It also should depict the concept of numbers such as 519 and 62. The image must convey the crossing over the boundaries of regular arithmetic operations, without containing any actual text.

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

Answer 1

To multiply (519 −−−√ ) (62 – √), we can simplify each radical expression first:

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

Now we can multiply the simplified expressions:

(√3 * √173) * (√2 * √31)

To multiply roots, we can multiply the numbers outside the root and multiply the numbers inside the root. So:

(√3 * √173) * (√2 * √31) = (√(3 * 173)) * (√(2 * 31)) = √(3 * 173 * 2 * 31)

Now we can simplify the expression inside the radical:

√(3 * 173 * 2 * 31) = √(3 * 2 * 31 * 173) = √(6 * 5393)

Since 6 is not a perfect square, we cannot simplify the expression any further.

Thus, the exact answer to (519 −−−√ ) (62–√) is √(6 * 5393).

Answer 2

To solve this question, you need to follow the order of operations (also known as PEMDAS).

First, calculate the square root of 519:
√519 ≈ 22.813

Next, calculate the square root of 62:
√62 ≈ 7.874

Now, you can multiply the two square roots:
(√519) * (√62) ≈ 22.813 * 7.874 ≈ 179.862

Therefore, the exact answer to the expression (519 −−−√ ) (62–√) is approximately 179.862.

Answer 3

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)