Expressing 1 2 + 3 + 5 with rational Denominator

Question

Expressing       1                  2            +              3            +              5             with rational Denominator

Dustin Durham · Accepted Answer

Hint:
First, multiply the expression with

\frac{(\sqrt{2} + \sqrt{3}) - \sqrt{5}}{(\sqrt{2} + \sqrt{3}) - \sqrt{5}}

What do you get as a result? Is the way forward clear to you? If not, post the result and we can see what to do in the next step.

Craig Mendoza · Accepted Answer

We can use the conjugate trick for rationalizing denominators more than once:      1                  2            +              3            +              5                                2            +              3            −              5                            2            +              3            −              5                        6              6        =                    2            +              3            −              5                    2              6                        6              6        =            2              3            +      3              2            −              30              12

Expressing 1 <msqrt> 2 </msqrt> + <msqrt>

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