Express in simplest radical form.
start fraction, square root of, 2646, end square root, divided by, square root of, 9, end square root, end fraction
2646/9
In simplest radical form, the expression becomes:
start fraction, square root of, 294, end square root, divided by, 3, end square root, end fraction
To express the value 2646 divided by 9 in simplest radical form, we need to simplify the square roots separately.
Let's start with the numerator: √2646.
First, we find the prime factorization of 2646: 2646 = 2 * 1323.
Next, we can simplify the square root using the property of square roots: √a * b = √a * √b. In this case, we can split the square root of 2646 into the square root of 2 and the square root of 1323. So √2646 = √2 * √1323.
To further simplify, we look for perfect square factors in the radicands. The perfect square factor of 2 is 1, and the perfect square factor of 1323 is 9. We can rewrite the square root of 2646 as: √2646 = √2 * √(9 * 147) = √2 * 3 * √147.
Moving on to the denominator: √9 = 3, since 9 is a perfect square.
Now, we can substitute the simplified square roots back into the original expression: (√2 * 3 * √147) divided by 3.
Notice that the 3 in the numerator and the denominator cancels out, leaving us with: √2 * √147.
Therefore, the simplified radical form of 2646/9 is √2 * √147.
To simplify the expression (2646/9), we can simplify the square roots separately before dividing.
Let's start with the numerator:
√2646 = √(2 ⋅ 3 ⋅ 7 ⋅ 53)
We can break down the square root into prime factors:
= √(2 ⋅ 3 ⋅ 7 ⋅ 53)
= √(2 ⋅ 3) ⋅ √(7 ⋅ 53)
= √2 ⋅ √3 ⋅ √7 ⋅ √53
Now let's simplify the denominator:
√9 = √(3 ⋅ 3)
Since 3 is a perfect square, we can simplify it further:
= 3
Putting it all together:
(2646/9) = (√2 ⋅ √3 ⋅ √7 ⋅ √53) / 3
So, the simplified expression is:
(√2 ⋅ √3 ⋅ √7 ⋅ √53) / 3
can I just have the answer in the simplest form
Apologies for the confusion. In simplest radical form, the expression 2646/9 simplifies to (√2 ⋅ √3 ⋅ √7 ⋅ √53) / 3.
What is the answer
The answer in simplest radical form is (√2 ⋅ √3 ⋅ √7 ⋅ √53) / 3.
Express in simplest radical form.
start fraction, square root of, 2646, end square root, divided by, square root of, 9, end square root, end fraction
9
2646
To express the expression in simplest radical form, we need to simplify the square roots separately and then divide.
Let's start with the numerator: √2646.
First, let's find the prime factorization of 2646: 2646 = 2 * 1323.
Next, we can simplify the square root using the property of square roots: √a * b = √a * √b. In this case, we can split the square root of 2646 into the square root of 2 and the square root of 1323. So, √2646 = √2 * √1323.
To further simplify, we look for perfect square factors in the radical. The perfect square factor of 2 is 1, and the perfect square factor of 1323 is 9. We can rewrite the square root of 2646 as: √2646 = √2 * √(9 * 147) = √2 * 3 * √147.
Now, let's simplify the denominator: √9 = 3.
Finally, we can substitute the simplified square roots back into the original expression: (√2 * 3 * √147) / 3.
Simplifying further, we can cancel out the common factor of 3 in the numerator and denominator, leaving us with: √2 * √147.
Therefore, the expression (√2646) / (√9) in simplest radical form is √2 * √147.