Show all of your steps for how to simplify 35√×210−−√

Question

. Your final answer should be in simplified radical form (not a decimal). Answers only with no work shown will receive no credit.

Answer 1

To simplify √35×√210, we can first simplify each square root separately.

√35 can be simplified as follows:
√35 = √(5×7) = √5×√7

√210 can be simplified as follows:
√210 = √(2×3×5×7) = √(2×3)×√(5×7) = √6×√(35)

Now, we can substitute the simplified values back into the original expression:
√35×√210 = (√5×√7)×(√6×√(35))

Since multiplication is commutative, we can rearrange the terms:
= √5×√7×√6×√(35)

Applying the product rule of square roots, we can combine the terms under a single square root:
= √(5×7×6×35)

Simplifying the expression inside the square root:
= √(5×7×6×5×7) = √(5^2×6×7^2)

Using the square root rule, we can take out the square factors:
= 5×7√(6)

Therefore, the simplified form of √35×√210 is 5×7√6.