Express in simplest radical form.
2, square root of, 200, end square root, minus, 10, square root of, 2, end square root
2
200
−10
2
2√200 - 10√2
To simplify this expression, we need to find any perfect square factors in the radical.
√200 = √(100 × 2) = √100 × √2 = 10√2
Now we can substitute this value back into the expression:
2(10√2) - 10√2
20√2 - 10√2
The two radical terms have the same radical, so we can combine them:
(20 - 10)√2
10√2
Therefore, the expression simplifies to 10√2.
To express this expression in the simplest radical form, we need to simplify both square roots separately and then subtract the simplified expressions.
First, let's simplify the square root of 200:
To simplify the square root of 200, we need to find the largest perfect square that is a factor of 200. The largest perfect square that is a factor of 200 is 100. So we can rewrite 200 as 100 * 2.
Therefore, square root of 200 can be simplified as the square root of 100 times the square root of 2:
√200 = √(100 * 2)
The square root of 100 is 10, so we have:
√200 = 10√2
Now, let's simplify the square root of 2:
The square root of 2 cannot be simplified any further, so we have:
√2
Now, we can subtract the simplified expressions:
10√2 - √2
Since the two expressions have the same radical term, we can subtract the coefficients:
10 - 1 = 9
Therefore, the expression 2√200 - √10 can be simplified as 9√2.
To express the expression (2√200 - 10√2) in simplest radical form, you need to simplify each square root separately, combine like terms, and then simplify further if possible.
Let's start with simplifying the square roots:
√200 can be simplified as follows:
√200 = √(100 * 2) = √100 * √2 = 10√2
Similarly, √2 cannot be simplified any further.
Now, let's substitute these simplifications back into the original expression:
(2 * 10√2 - 10√2)
Combining like terms, we have:
(20√2 - 10√2)
Simplifying further, we get:
10√2
Therefore, the expression (2√200 - 10√2) simplifies to 10√2.
Express in simplest radical form.
minus, 5, square root of, 5, end square root, minus, 4, square root of, 5, end square root
−5
5
−4
5
To express the expression (-5√5 - 4√5) in simplest radical form, we need to combine the like terms.
Both terms have the same radical, which is √5. So we can combine the coefficients:
(-5 - 4)√5
Simplifying further:
-9√5
Therefore, the expression (-5√5 - 4√5) simplifies to -9√5.
Express in simplest radical form.
minus, 5, square root of, 6, end square root, minus, 7, square root of, 6, end square root
−5
6
−7
6
To express the expression (-5√6 - 7√6) in simplest radical form, we need to combine the like terms.
Both terms have the same radical, which is √6. So we can combine the coefficients:
(-5 - 7)√6
Simplifying further:
-12√6
Therefore, the expression (-5√6 - 7√6) simplifies to -12√6.