Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

How do I square root this?

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how do you square root(6+4root2)

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Original post by sdfsdd

how do you square root(6+4root2)

Say that

6+4\sqrt{2}=(a+b\sqrt{2})^2

then expand the RHS to get

a^2+2b^2+2ab\sqrt{2}

Then compare rationals and irrationals between the two sides to get

6=a^2+2b^2

and

4=2ab

then just solve simultaneously for

a,b

and so

\sqrt{6+4\sqrt{2}}=a+b\sqrt{2}

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OP

Original post by RDKGames

Say that

6+4\sqrt{2}=(a+b\sqrt{2})^2

then expand the RHS to get

a^2+2b^2+2ab\sqrt{2}

Then compare rationals and irrationals between the two sides to get

6=a^2+2b^2

and

4=2ab

then just solve simultaneously for

a,b

and so

\sqrt{6+4\sqrt{2}}=a+b\sqrt{2}

thx that was really helpful

Original post by RDKGames

Then compare rationals and irrationals between the two sides to get

6=a^2+2b^2

and

4=2ab

then just solve simultaneously for

a,b

and so

\sqrt{6+4\sqrt{2}}=a+b\sqrt{2}

It's perhaps worth mentioning that if you have reason to believe there's a "nice" solution, it's generally a *lot* quicker to make some educated guesses for a, b than it is to solve algebraically. (e.g. for this question you can spot what a, b must be in about 15 seconds just by guessing).

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