What is the product of 7, square root of, 6, end square root7
6
and 7, square root of, 14, end square root7
14
in simplest radical form?
To find the product of these two expressions, we multiply the numbers outside the square root together and then multiply the numbers inside the square root together.
The product of 7 and 14 is 7 * 14 = 98.
The product of square root of 6 and square root of 7 is √6 * √7 = √(6 * 7) = √42.
Therefore, the product of the two expressions in simplest radical form is 98√42.
To find the product of 7√6 and 7√14 in simplest radical form, we can multiply the numbers outside the square roots and multiply the numbers inside the square roots separately.
First, let's multiply the numbers outside the square roots:
7 * 7 = 49.
Next, let's multiply the numbers inside the square roots:
√6 * √14 = √84.
Now, let's simplify the square root of 84:
√84 = √(4 * 21) = √4 * √21 = 2√21.
Finally, putting it all together, the product of 7√6 and 7√14 in simplest radical form is:
49 * 2√21 = 98√21.
To find the product of these two expressions in simplest radical form, we can multiply the numbers outside the square root sign and multiply the numbers inside the square root sign. Let's calculate it step by step.
First, let's multiply the numbers outside the square root:
7 * 14 = 98
Next, let's multiply the numbers inside the square root:
√6 * √7 = √42
Now, let's put it all together:
98 * √42
However, we can simplify the square root of 42 further. To simplify, we look for perfect square factors of 42. The perfect square factors of 42 are 1, 4, 9, and 36. Since 42 does not have any perfect square factors, we cannot simplify it any further.
Therefore, the product of 7√6 and 7√14 in simplest radical form is:
98√42
give me the simplest form
Apologies for the confusion. Let's simplify the expression further.
The square root of 42 can be simplified by breaking it down into factors that include a perfect square. The factors of 42 that are perfect squares are 1, 4, and 9.
Therefore, we can rewrite the square root of 42 as the square root of (6*7) which is the same as the square root of 6 multiplied by the square root of 7.
So, 7√6 * 7√14 simplifies to 7 * √(6*7) * √14 = 7√(6*7*14) = 7√(588).
Upon further simplification, we can find that the square root of 588 is equal to the square root of (4*147), which can be written as the square root of 4 multiplied by the square root of 147.
The square root of 4 is simply 2, and the square root of 147 cannot be simplified any further.
Therefore, the simplest form of 7√6 * 7√14 is: 2 * 7 * √147 = 14√147.