reviewing an old question

[yfelix45]

hello,

Thanks to all on this message board for all the help I have received.


This is an old question that I am confused about mistakes I have made.

simplify:
-6v(80) +2v(75) - 8 v(245) – 14v(108)

This is my simplification:

-6v(80) +2v(75) - 8 v(245) – 14v(108)
= -6v2*40 + 2v3*25 – 8 v7 *35 – 14v9*12

= - 6v2v4*10 + 2v3v5 – 8 v7 v7*5 – 14v3v3*4

= - 6v2v2v2*5 + 2v3v5 – 8 v7 v7v5 – 14v3v3v4

= -6(2v5) + 2(3v5) – 8 (7v5) – 14(3v2)

= -12v5 + 6v5 – 56 v5 – 42(v2)

= -12 + 6 – 56 v5 – 42 v2

= -62 v5 – 42 v2

Can you help explain what I did wrong?
thanks

yfelix45

* v: this is sqrt. I copied and pasted what I did from my folder

 

[Novice]

I have seen just one mistake, maybe there are a lot more similar careless mistakes.

-6v(80) +2v(75) - 8 v(245) – 14v(108)
= -6v2*40 + 2v3*25 – 8 v7 *35 – 14v9*12

= - 6v2v4*10 + 2v3v5 – 8 v7 v7*5 – 14v3v3*4

Now tell me, can √(3*25) be written as (√3) * (√5) as you have done?

You need to solve the problem from scratch, and very very carefully to get the correct answer.

 

[soroban]

Hello, yfelix45!

Your radical-work is off . . .

\(\displaystyle \text{Simplify: }\;-6\sqrt{80} + 2\sqrt{75} - 8\sqrt{245} - 14\sqrt{108}\)

Let's simplify each radical separately.

. . \(\displaystyle \begin{array}{ccccccc}\sqrt{80} &=& \sqrt{16\cdot5} &=& \sqrt{16}\sqrt{5} &=& 4\sqrt{5} \\ \sqrt{75} &=& \sqrt{25\cdot3} &=& \sqrt{25}\sqrt{3} &=& 5\sqrt{3} \\
\sqrt{245} &=& \sqrt{49\cdot5} &=& \sqrt{49}\sqrt{5} &=& 7\sqrt{5} \\ \sqrt{108} &=& \sqrt{36\cdot3} &=& \sqrt{36}\sqrt{3} &=& 6\sqrt{3}\end{array}\)


Then the problem becomes:

. . \(\displaystyle -6(4\sqrt{5}) + 2(5\sqrt{3}) - 8(7\sqrt{5}) - 14(6\sqrt{3}) \)

. . \(\displaystyle =\;-24\sqrt{5} + 10\sqrt{3} - 56\sqrt{5} - 84\sqrt{3}\)

. . \(\displaystyle =\; -80\sqrt{5} - 74\sqrt{3}\)

 

[yfelix45]

thank you and comments

Hello,

To Soroban: Thank you for your help in showing me where I went wrong. The answer you gave was correct I just needed to know where exactly I went wrong.

To Denis: Thank you for further breaking down the answer.

To novice: While I thank you for pointing out my mistake, I did redo the question from scratch to find my error before I came to message board for help. I often come to the message board for help when I need another opinion on how to proceed with solving the problem. If you did not want to help with the question, why answer?


Thanks

yfelix45