# simplying and factoring

by Greg
(New England)

7x^3 3/125x^4+3/x^7

the / meant to be square roots

### Comments for simplying and factoring

 Jan 12, 2011 Simplifying & Factoring Radical Expressions by: Staff The question: by Greg (New England) 7x^3 3/125x^4+3/x^7 the / meant to be square roots The answer: 7x^3 3/125x^4+3/x^7 the / meant to be square roots ------------------------------------------------------------------------------------------ Standard square root terminology - for future reference any number raised to the ½ power stands for the square root of that number e.g.: x^(1/2) = the square root of x = sqrt(x) any number raised to the 1/3 power stands for the cube root of that number any number raised to the ¼ power stands for the 4th root of that number and so on … ------------------------------------------------------------------------------------------ 7x^3 3/125x^4+3/x^7 the / meant to be square roots You didn’t indicate what the relationship is (+ or – or *) between the 7x^3 and the 3/125x^4 Since there is a blank space in between, I’m going to assume you meant these two expressions are multiplied 7x^3 3/125x^4+3/x^7 the / meant to be square roots (7x^3)*3*sqrt(125x^4)+3*sqrt(x^7) To simplify this expression, begin by factoring the sqrt portions (7x^3)*3*sqrt(125x^4)+3*sqrt(x^7) (7x^3)*3*sqrt(5*5*5*x*x*x*x)+3*sqrt(x*x*x*x*x*x*x) Next, group the values under the square root signs as squares (7x^3)*3*sqrt(5*5*5*x*x*x*x)+3*sqrt(x*x*x*x*x*x*x) (7x^3)*3*sqrt[5*(5^2)*(x^2)*x^2)]+3*sqrt[x*(x^2)*(x^2)*(x^2)] Now split the expressions under the square root signs into separate square roots which are multiplied together (7x^3)*3*sqrt(5)*sqrt(5^2)*sqrt(x^2)*sqrt(x^2)+3*sqrt(x)*sqrt(x^2)*sqrt(x^2)*sqrt(x^2) Evaluate the square root where possible Note: the sqrt(x^2) = x, the sqrt(5^2) = 5 (7x^3)*3*sqrt(5)*sqrt(5^2)*sqrt(x^2)*sqrt(x^2)+3*sqrt(x)*sqrt(x^2)*sqrt(x^2)*sqrt(x^2) (7x^3)*3*sqrt(5)*5*x*x+3*sqrt(x)*x*x*x (7x^3)*3*sqrt(5)*5*x*x+3*sqrt(x)*x*x*x (7x^3)*3*sqrt(5)*5*x^2+3*sqrt(x)* x^3 (7x^3)*3*5*(x^2)*sqrt(5)+3*(x^3)*sqrt(x) 7*(x^3)*(x^2)*15*sqrt(5)+3*(x^3)*sqrt(x) 7*15*(x^3)*(x^2)*sqrt(5)+3*(x^3)*sqrt(x) 105*(x^5)*sqrt(5)+3*(x^3)*sqrt(x) The final answer: 105*(x^5)*sqrt(5)+3*(x^3)*sqrt(x) You can’t simplify the expression past this point. However, you can factor out the 3*(x^3) if you wish. If you factor out the 3*(x^3), the expression will look like this: [3*(x^3)]*[35*(x^2)*sqrt(5)+ sqrt(x)] Thanks for writing. Staff www.solving-math-problems.com