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# Help. ​

+1
54
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+1714

Help.

NotSoSmart  Jan 30, 2018
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#1
+82863
+2

3√750 + 3√2058  +  3√48

The trick here, NSS...is to simplify the radicands as much as we can...let's factor these, first

750  =  250 * 3   =   25 * 10 * 3   =  5^2 * 5 * 2 * 3  =  5^3 * 6

2058  =   1029 * 2   =  343 * 3 * 2  =  7^3 * 6

48  =  8 * 6  =  2^3 * 6

So  we have

3√ [ 5^3 * 6 ] + 3√ [ 7^3 * 6 ]  + 3√ [ 2^3 * 6 ]  =

53√6  + 73√6  + 23√6

Now just add the coefficients in front of each radical and let the radical go along for the ride..so we have

[ 5 + 7 + 2 ] 3√6  =

143√6

CPhill  Jan 30, 2018
#2
+6351
+3

4.

$$\quad\,(7-\sqrt7)(-6+\sqrt7) \\~\\ =\,(7)(-6)+(7)(\sqrt7)+(-\sqrt7)(-6)+(-\sqrt7)(\sqrt7) \\~\\ =\,-42+7\sqrt7+6\sqrt7-7 \\~\\ =\,-49+13\sqrt7$$

hectictar  Jan 30, 2018

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