Multiply (519 −−−√ ) (62–√) . Give an exact answer.(1 point)
To find an exact answer, we need to simplify the given expression.
We are given:
(519 −−−√ ) (62–√)
Let's simplify each term separately.
1) √519:
To simplify the square root of 519, we need to find its prime factors:
519 = 3 * 173
Since there are no perfect square factors, we cannot simplify the square root of 519 any further.
2) (62–√):
We don't know the exact value of √62, so we cannot simplify this term any further.
Now, let's multiply the simplified terms:
(519 −−−√ ) (62 – √) = √519*(62 – √)
Since we cannot simplify further, the expression √519*(62 – √) is the exact answer.
To solve this problem, we need to simplify each square root expression and then multiply the resulting expressions together.
Let's start by simplifying the square root expressions:
√519 is an irrational number because 519 is not a perfect square. It cannot be simplified further.
√62 is also an irrational number because 62 is not a perfect square. It cannot be simplified further either.
Now, we can multiply the simplified expressions:
(519 −−−√ ) (62–√) = (√519) (√62)
Multiplying these two expressions together:
(√519) (√62) = √(519 × 62)
To find the exact answer, we need to find the product of 519 and 62 under the square root:
√(519 × 62) = √(32178)
The square root of 32178 is an irrational number because 32178 is not a perfect square. As a result, the final answer, when being left in exact form, is √(32178).