SOLUTION: I really need some help with multiply and divide the radical expression Square7 (2 square3+ 3 square7) and 18+square567 over 9 thank you for your help[

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Question 90220: I really need some help with multiply and divide the radical expression
Square7 (2 square3+ 3 square7)
and
18+square567 over 9
thank you for your help[
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%287%29%2A%282%2Asqrt%283%29%2B3%2Asqrt%287%29%29 Start with the expression

sqrt%287%29%2A2%2Asqrt%283%29%2Bsqrt%287%29%2A3%2Asqrt%287%29%29 Distribute

2%2Asqrt%287%2A3%29%2B3%2Asqrt%287%2A7%29%29 Multiply the square roots

2%2Asqrt%2821%29%2B3%2Asqrt%2849%29%29 Multiply

2%2Asqrt%2821%29%2B3%2A7%29 Take the square root

2%2Asqrt%2821%29%2B21%29 Multiply

So the expression
sqrt%287%29%2A%282%2Asqrt%283%29%2B3%2Asqrt%287%29%29


simplifies to

2%2Asqrt%2821%29%2B21%29


==================================================================
Start with the expression
%2818+%2B+sqrt%28567%29%29%2F9

First lets reduce sqrt%28567%29
-----------------------------------------------------
sqrt%28567%29 Start with the given expression
The goal of simplifying expressions with square roots is to factor the radicand into a product of two numbers. One of these two numbers must be a perfect square. This way the perfect square will become a rational number.
So let's list the factors of 567
Factors:
1, 3, 7, 9, 21, 27, 63, 81, 189,


Notice how 81 is the largest perfect square, so lets break 567 down into 81*7


sqrt%2881%2A7%29 Factor 567 into 81*7

sqrt%2881%29%2Asqrt%287%29 Break up the square roots using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29

9%2Asqrt%287%29 Take the square root of the perfect square 81 to get 9

So the expression

sqrt%28567%29

simplifies to

9%2Asqrt%287%29
-----------------------------------------------------

%2818+%2B+9%2Asqrt%287%29%29%2F9 Simplify the square root (using the technique above)

18%2F9+%2B+9%2Asqrt%287%29%2F9 Break up the fraction

2+%2B+9%2Asqrt%287%29%2F9 Divide 18%2F9 to get 2

2+%2B+sqrt%287%29 Divide 9%2F9 to get 1



So the expression
%2818+%2B+sqrt%28567%29%29%2F9

simplifies to

2+%2B+sqrt%287%29