SOLUTION: 2 sqrt 20 - 3 sqrt 7 - 2 sqrt 5 +4 sqrt 63

Algebra ->  Radicals -> SOLUTION: 2 sqrt 20 - 3 sqrt 7 - 2 sqrt 5 +4 sqrt 63      Log On


   

Question 271329: 2 sqrt 20 - 3 sqrt 7 - 2 sqrt 5 +4 sqrt 63
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
2sqrt%28+20%29+-+3sqrt%28+7%29+-+2sqrt%28+5%29+%2B4sqrt%28+63%29
None of these terms are like terms. So we cannot do any adding or subtracting (yet).

But we should, as always, try to simplify the square roots. Simplifying square roots involves finding perfect square factors of the radicand (the expression inside the radical), if any. The first and last radicands have perfect square factors:
2sqrt%284%2A5%29+-+3sqrt%28+7%29+-+2sqrt%28+5%29+%2B4sqrt%289%2A7%29
Now we can use the property of radicals, root%28a%2C+p%2Aq%29+=+root%28a%2C+p%29+%2A+root%28a%2C+q%29, to separate out the perfect square factors into their own square roots:
2sqrt%284%29%2Asqrt%285%29+-+3sqrt%28+7%29+-+2sqrt%28+5%29+%2B+4sqrt%289%29%2Asqrt%287%29
Next we simplify the square roots of the perfect squares:
2%2A2sqrt%285%29+-+3sqrt%28+7%29+-+2sqrt%28+5%29+%2B4%2A3sqrt%287%29
which simplifies to:
4sqrt%285%29+-+3sqrt%28+7%29+-+2sqrt%28+5%29+%2B+12sqrt%287%29
Not only have we been able to simplify the square roots, we now have like terms to add or subtract. Just like 4x - 2x = 2x, 4sqrt%285%29+-+2sqrt%28+5%29+=+2sqrt%285%29. And just like -3x + 12x = 9x, -3sqrt%28+7%29+%2B+12sqrt%287%29+=+9sqrt%287%29. So our final answer is
2sqrt%285%29+%2B+9sqrt%287%29