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

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

 Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations! Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

 Algebra: Polynomials, rational expressions and equations Solvers Lessons Answers archive Quiz In Depth

 Question 604245: explain the squareroot of 180 minus the squareroot of 5Found 2 solutions by flame8855, bucky:Answer by flame8855(424)   (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)   (Show Source): You can put this solution on YOUR website!The problem you are given is to simplify: . . 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: . . 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: . . Next, note that the square root of 36 is 6. Substituting 6 for the square root of 36 results in: . . 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: . . and in the parentheses you can subtract 1 from 6 to get 5. Substituting this 5 for (6 - 1) gives the answer: . . 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. .