SOLUTION: . Rationalize the denominator: 2____ √[6] – √[5] It came out fuzzy I will retype it 2/sqrt[6]-[5] . Simplify the ration

Algebra ->  Radicals -> SOLUTION: . Rationalize the denominator: 2____ √[6] – √[5] It came out fuzzy I will retype it 2/sqrt[6]-[5] . Simplify the ration      Log On


   

Question 188648: . Rationalize the denominator:
2____
√[6] – √[5]

It came out fuzzy I will retype it

2/sqrt[6]-[5]

. Simplify the rational expression:
x2 – 3x – 10 find the gcf of the polynomial
x2 – x – 20




. Simplify:
√[144x10y12z18]

Found 2 solutions by Alan3354, jim_thompson5910:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Rationalize the denominator:
2____
√[6] – √[5]
It came out fuzzy I will retype it
2/sqrt[6]-[5]
I think you mean
2%2F%28sqrt%286%29+-+sqrt%285%29%29
Multiply NUM and DEN by the conjugate of the DEN
The conjugate is %28sqrt%286%29+%2B+sqrt%285%29%29, a sign change.
= 2%28sqrt%286%29+%2B+sqrt%285%29%29%2F%286-5%29
= 2sqrt%286%29+%2B+2sqrt%285%29
-----------------------
. Simplify the rational expression:
x2 – 3x – 10 find the gcf of the polynomial
x2 – x – 20
---------------
If you mean the GCF of the 2 polynomials:
x^2 – 3x – 10 = (x-5)*(x+2)
x^2 – x – 20 = (x-5)*(x+4)
------------
The only common factor is (x-5), so that's the GCF.
-----------------
. Simplify:
√[144x10y12z18]
I think you mean:
sqrt%28144x%5E10y%5E12z%5E18%29
= 12x%5E5y%5E6z%5E9


Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1


2%2F%28+sqrt%286%29-sqrt%285%29+%29+ Start with the given expression.


Multiply both the numerator and denominator by sqrt%286%29%2Bsqrt%285%29 (the conjugate of the denominator). This will rationalize the denominator


FOIL


%282%28+sqrt%286%29%2Bsqrt%285%29+%29%29%2F%28+6-5+%29 Square each term.


%282%28+sqrt%286%29%2Bsqrt%285%29+%29%29%2F%28+1+%29 Subtract


2%28+sqrt%286%29%2Bsqrt%285%29+%29 Reduce


2%2Asqrt%286%29%2B2%2Asqrt%285%29 Distribute


So 2%2F%28+sqrt%286%29-sqrt%285%29+%29+=+2%2Asqrt%286%29%2B2%2Asqrt%285%29+





# 2




%28x%5E2-3x-10%29%2F%28x%5E2-x-20%29 Start with the given expression.


%28%28x%2B2%29%2A%28x-5%29%29%2F%28x%5E2-x-20%29 Factor x%5E2-3x-10 to get %28x%2B2%29%2A%28x-5%29.


%28%28x%2B2%29%2A%28x-5%29%29%2F%28%28x%2B4%29%2A%28x-5%29%29 Factor x%5E2-x-20 to get %28x%2B4%29%2A%28x-5%29.


%28%28x%2B2%29highlight%28%28x-5%29%29%29%2F%28%28x%2B4%29highlight%28%28x-5%29%29%29 Highlight the common terms.


%28%28x%2B2%29cross%28%28x-5%29%29%29%2F%28%28x%2B4%29cross%28%28x-5%29%29%29 Cancel out the common terms. Note: the GCF is x-5 and is canceled out.


%28x%2B2%29%2F%28x%2B4%29 Simplify.


So %28x%5E2-3x-10%29%2F%28x%5E2-x-20%29 simplifies to %28x%2B2%29%2F%28x%2B4%29.


In other words, %28x%5E2-3x-10%29%2F%28x%5E2-x-20%29=%28x%2B2%29%2F%28x%2B4%29 where x%3C%3E-4 or x%3C%3E5





# 3




sqrt%28144%2Ax%5E10%2Ay%5E12%2Az%5E18%29 Start with the given expression.


sqrt%28144%2Ax%5E2%2Ax%5E2%2Ax%5E2%2Ax%5E2%2Ax%5E2%2Ay%5E12%2Az%5E18%29 Factor x%5E10 into x%5E2%2Ax%5E2%2Ax%5E2%2Ax%5E2%2Ax%5E2


Factor y%5E12 into y%5E2%2Ay%5E2%2Ay%5E2%2Ay%5E2%2Ay%5E2%2Ay%5E2


Factor z%5E18 into z%5E2%2Az%5E2%2Az%5E2%2Az%5E2%2Az%5E2%2Az%5E2%2Az%5E2%2Az%5E2%2Az%5E2


Break up the square root using the identity sqrt%28A%2AB%29=sqrt%28A%29%2Asqrt%28B%29.


Take the square root of 144 to get 12.


Take the square root of x%5E2 to get x.


Take the square root of y%5E2 to get y.


12%2Ax%2Ax%2Ax%2Ax%2Ax%2Ay%2Ay%2Ay%2Ay%2Ay%2Ay%2Az%2Az%2Az%2Az%2Az%2Az%2Az%2Az%2Az Take the square root of z%5E2 to get z.


12x%5E5y%5E6z%5E9 Rearrange and multiply the terms.

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Answer:


So sqrt%28144%2Ax%5E10%2Ay%5E12%2Az%5E18%29 simplifies to 12x%5E5y%5E6z%5E9


In other words, sqrt%28144%2Ax%5E10%2Ay%5E12%2Az%5E18%29=12x%5E5y%5E6z%5E9 where every variable is non-negative.