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.
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.
To simplify the expression 35√×210−−√, we can break it down into smaller steps.
Step 1: Simplify the square root of 210:
To simplify √210, we need to determine the factors of 210. The factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, and 210.
However, we are looking for perfect square factors. The perfect square factors of 210 are 1, 4, 9, 16, 25, 36, 49, 64, and 81. Since none of the factors of 210 are perfect squares, we cannot simplify √210 any further.
Step 2: Simplify the product of 35 and √210:
To simplify 35√210, we can rewrite it as 35 * √210.
Step 3: Combine the radical terms:
Since we cannot simplify √210 any further, we can't combine the radical terms. So the final answer is 35√210.
Therefore, the simplified form of 35√×210−−√ is 35√210.
To simplify the expression 35√×210−−√, we can break it down into two separate radicals and simplify each one individually.
Step 1: Simplify the first radical, 35√.
To find the simplified form of this radical, we need to determine the largest perfect square that divides evenly into 35. The largest perfect square that divides evenly into 35 is 5, because 5^2 = 25. So, we can rewrite 35 as 5 * 7.
Now, rewriting the radical as 5 * 7√ will give us: 5 * 7√×210−−√.
Step 2: Simplify the second radical, 210−−√.
Similar to the first step, we need to find the largest perfect square that divides evenly into 210. The largest perfect square that divides evenly into 210 is 2, because 2^2 = 4.
So, we can rewrite 210 as 2 * 2 * 3 * 5 * 7.
Now, rewriting the radical as 5 * 7√×2 × 2 * 3 * 5 * 7−−√ will give us: 5 * 7√×2 × 2 * 3 * 5 * 7−−√.
Step 3: Multiply the constants outside the radicals.
Multiplying the constants 5 and 7 together, we get 35 as the product.
So, our expression becomes: 35 * 7√×2 × 2 * 3 * 5 * 7−−√.
Step 4: Combine the radical terms inside the square root.
Inside the square root, we have 2 * 2 * 3 * 5 * 7, which simplifies to 2^2 * 3 * 5 * 7.
So, our expression becomes: 35 * 7√×2^2 * 3 * 5 * 7.
Step 5: Simplify the square root term.
The square root of 2^2 is 2, because 2^2 = 4.
So, our expression becomes: 35 * 7√×4 * 3 * 5 * 7.
Step 6: Multiply the constants together.
Multiplying the constants together, we get 4 * 3 * 5 * 7 = 420.
So, the final simplified form of the expression 35√×210−−√ is 35 * 7 * 2√×420.