SOLUTION: I need to simpfifly radical expressions(no calculator) 1. 2sqrt(75) + sqrt(108) 2. sqrt(6)( sqrt(3)+5 sqrt(2) ) 3. (3- sqrt(2)(3 + sqrt(2) ) 4. 3 sqrt(2) ------

Algebra ->  Radicals -> SOLUTION: I need to simpfifly radical expressions(no calculator) 1. 2sqrt(75) + sqrt(108) 2. sqrt(6)( sqrt(3)+5 sqrt(2) ) 3. (3- sqrt(2)(3 + sqrt(2) ) 4. 3 sqrt(2) ------      Log On


   

Question 312691: I need to simpfifly radical expressions(no calculator)
1. 2sqrt(75) + sqrt(108)

2. sqrt(6)( sqrt(3)+5 sqrt(2) )
3. (3- sqrt(2)(3 + sqrt(2) )
4. 3 sqrt(2)
---------
5+ sqrt(3)
5.sqrt(5x+1)+2=6

please show me how you get thee answers
thank you! p.s. number 4. the --- is the division line
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
I need to simplifly radical expressions(no calculator)
1. 2sqrt%2875%29+%2B+sqrt%28108%29
Factor inside the radicals to reveal perfect squares
2%2Asqrt%2825%2A3%29+%2B+sqrt%2836%2A3%29
Extract the squares
5%2A2sqrt%283%29+%2B+6%2Asqrt%283%29
10%2Asqrt%283%29+%2B+6%2Asqrt%283%29
these are like terms so we just add them
16%2Asqrt%283%29
:
2. sqrt%286%29%28+sqrt%283%29%2B5sqrt%282%29+%29
multiply what's inside the brackets
sqrt%286%2A3%29%2B5sqrt%286%2A2%29
sqrt%2818%29%2B5sqrt%2812%29
Factor to reveal perfect squares
sqrt%289%2A2%29%2B5sqrt%284%2A3%29
Extract those squares
3%2Asqrt%282%29%2B2%2A5sqrt%283%29
3%2Asqrt%282%29%2B10%2Asqrt%283%29
:
3. %283-sqrt%282%29%29%2A%283%2Bsqrt%282%29%29
FOIL
9+%2B+3sqrt%282%29+-+3sqrt%282%29+-+2
Middle terms cancel
9 - 2 = 7
:
4. %283sqrt%282%29%29%2F%285%2B+sqrt%283%29%29
multiply by the conjugate of the denominator over itself
:%283sqrt%282%29%29%2F%285%2B+sqrt%283%29%29 * %285-sqrt%283%29%29%2F%285-+sqrt%283%29%29 = %2815sqrt%282%29-3sqrt%283%2A2%29%29%2F%2825-3%29 = %2815sqrt%282%29-3sqrt%286%29%29%2F%2822%29
:
5.sqrt%285x%2B1%29%2B2=6+
subtract 2 from both sides
sqrt%285x%2B1%29=4+
Square both sides
5x + 1 = 16
5x = 16 - 1
5x = 15
x = 3
:
You can check solution in the original equation