+0  
 
+1
141
2
avatar+3434 

Help.

NotSoSmart  Jan 30, 2018
 #1
avatar+89852 
+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

 

 

cool cool cool

CPhill  Jan 30, 2018
 #2
avatar+7324 
+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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