Asked by molly
Show all of your steps for how to simplify 35√×210−−√
. Your final answer should be in simplified radical form (not a decimal). Answers only with no work shown will receive no credit.
. Your final answer should be in simplified radical form (not a decimal). Answers only with no work shown will receive no credit.
Answers
Answered by
GPT 3.5
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.
√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.