SOLUTION: explain the squareroot of 180 minus the squareroot of 5

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: explain the squareroot of 180 minus the squareroot of 5      Log On


   

Question 604245: explain the squareroot of 180 minus the squareroot of 5
Found 2 solutions by flame8855, bucky:
Answer by flame8855(424) About Me  (Show Source):
You can put this solution on YOUR website!
180 = 5* 6*6
so sqaureroot 180 = 6sqrt5
squareroot of 180 minus the squareroot of 5 = 5squareroot5 = 5sqrt5

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
The problem you are given is to simplify:
.
sqrt%28180%29+-+sqrt%285%29
.
Begin by factoring the 180. Since this problem has the goal of teaching you something about simplifying radicals, you can assume the likelihood that 5 is a good factor to try and that somehow the square root of 5 will be involved in both terms of the expression you are given. So factoring 5 from 180 results in the two term expression becoming:
.
sqrt%2836%2A5%29+-+sqrt%285%29
.
But, by the rules of radicals, the first term can now become the product of the radicals of the two factors and the expression is then:
.
sqrt%2836%29%2Asqrt%285%29+-+sqrt%285%29
.
Next, note that the square root of 36 is 6. Substituting 6 for the square root of 36 results in:
.
6%2Asqrt%285%29+-+sqrt%285%29
.
Then note that the square root of 5 is a common factor of both terms. If you factor it from both of the terms you get the distributed multiplication:
.
%286+-+1%29%2Asqrt%285%29
.
and in the parentheses you can subtract 1 from 6 to get 5. Substituting this 5 for (6 - 1) gives the answer:
.
5%2Asqrt%285%29
.
And this is a step-by-step method of solving the given problem.
.
I hope this helps you to understand some procedures you can use when working with radicals to simplify algebraic expressions.
.