Respuesta :

gabby5792

Your problem looks like this

[tex]11\sqrt{45}  - 4\sqrt{5}[/tex]

To make this problem easier, we need to simplify these square roots

[tex]11\sqrt{45}[/tex]    can be simplified

Here's how :

The factors of 45 are 9 and 5

9 is a perfect square root, but 5 is not

Think of the problem like this

[tex]\sqrt{9}     ×     \sqrt{5}[/tex]

The square root of 9 is 3, but 5 has no perfect square root

Now [tex]11\sqrt{45}[/tex] is simplified to [tex]33\sqrt{5}[/tex]

Now let's solve the problem, because we have a common square root of 5

[tex]33\sqrt{5}[/tex] - 4\sqrt{5}[/tex]

Our final answer is

[tex]29\sqrt{5}[/tex]

Feel free to ask questions if you are confused! Hope I helped :)

carlosego

For this case we must simplify the following expression:

[tex]11 \sqrt {45} -4 \sqrt {5}[/tex]

So, we rewrite 45 as [tex]3 ^ 2 * 5[/tex]:

[tex]11 \sqrt {3 ^ 2 * 5} -4 \sqrt {5} =[/tex]

We have by definition of properties of powers and roots that:

[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

So:

[tex]11 * 3 \sqrt {5} -4 \sqrt {5} =\\33 \sqrt {5} -4 \sqrt {5} =\\29 \sqrt {5}[/tex]

Answer:

[tex]29 \sqrt {5}[/tex]

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