Question

Simplify three square root of five end root minus two square root of seven end root plus square root of forty five end root minus square root of twenty eight. two square root of twelve two square root of two six square root of five end root minus four square root of seven six square root of ten end root minus four square root of fourteen

Answer 1

Answer:

$6\sqrt{5}-4\sqrt{7}$

Step-by-step explanation:

I am able to interpret only the first mathematical expression that you listed. The ones that follow are not clear.

Here it goes:

$3\sqrt{5} -2\sqrt{7} +\sqrt{45} -\sqrt{28} =\\3\sqrt{5} -2\sqrt{7} +\sqrt{9*5} -\sqrt{4*7}=\\3\sqrt{5} -2\sqrt{7} +3\sqrt{5} -2\sqrt{7}=\\6\sqrt{5}-4\sqrt{7}$

Notice that for the last two radical expressions that contain numbers that are not prime, we write:

a)  45 as the product 9*5, and then use the fact that 9 is the perfect square of 3, therefore 3 can be taken out of the square root as a multiplicative factor.

b) 28 as he product 4*7, and then use the fact that 4 is the perfect square of 2, therefore 2 can be extracted out of the square root as a multiplicative factor.

Then we are able to combine together all the terms that contain $\sqrt{5}$; and also among themselves all those terms that contain $\sqrt{7}$.

We end up with the following simplified expression:

$6\sqrt{5}-4\sqrt{7}$

Answer 2

Answer:

3. $\sqrt[6]{5} - \sqrt[4]{7}$

Step-by-step explanation:

It was correct in the test.

Please, please, please mark the person above me brainliest. The user deserves it. Mbe... took their time to explain it step-by-step.

Have a great day! :D

P.S the only reason why I didn't put the full username is because brainly marked it as a swear word, lol