Respuesta :
Solution:
The simplified form of the radical expression is [tex]-9\sqrt5 [/tex]
Explanation:
We have been given the radical expression [tex]-2\sqrt{20}-\sqrt{125}[/tex]
First of all, we find the factors of 20 and 125
[tex]20=4 \times 5\\\\125 = 25 \times 5[/tex]
On plugging these values in the given expression, we get
[tex]-2\sqrt{4 \times 5}-\sqrt{ 25 \times 5}[/tex]
We know that square root of 4 is 2 and square root of 25 is 5. Hence, we have
[tex]2\times 2 \sqrt 5 - 5\sqrt 5\\\\-4\sqrt5 - 5\sqrt 5\\\\-9\sqrt5[/tex]
Therefore, the simplified form of the radical expression is [tex]-9\sqrt5[/tex]
Answer:
[tex]-9\sqrt{5}[/tex]
Step-by-step explanation:
We have:
[tex]-2\sqrt{20} -\sqrt{125}[/tex]
Now, we need to transform each sub-radical number in another pair of numbers that allow us to simplify each radical into a common radical.
So, we know that 20=4(5), and 125=25(5).
Replacing these in the expression:
[tex]-2\sqrt{4(5)}-\sqrt{25(5)}[/tex]; but 4 and 25 have squared roots.
Then:
[tex]-2(2)\sqrt{5} -5\sqrt{5}\\ -4\sqrt{5}-5\sqrt{5}[/tex]
Now, we can operate these terms, because they are like terms, that is, they have the same root. Therefore, the simplest radical form is:
[tex]-9\sqrt{5}[/tex]
