SOLUTION: Use Property 1 to simplify each of the following radical expressions. Assume that all variables represent positive real numbers. sqrt200y^6 sqrt(5m^2)/2

Algebra ->  Expressions-with-variables -> SOLUTION: Use Property 1 to simplify each of the following radical expressions. Assume that all variables represent positive real numbers. sqrt200y^6 sqrt(5m^2)/2       Log On


   

Question 109224: Use Property 1 to simplify each of the following radical expressions. Assume that all variables represent positive real numbers.
sqrt200y^6
sqrt(5m^2)/2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
#1
sqrt%28200%2Ay%5E6%29Start with the given expression
sqrt%28100%2A2%2Ay%5E6%29 Factor 200 into 100%2A2

sqrt%28100%2A2%2Ay%5E2%2Ay%5E2%2Ay%5E2%29 Factor y%5E6 into y%5E2%2Ay%5E2%2Ay%5E2

sqrt%28100%29%2Asqrt%282%29%2Asqrt%28y%5E2%29%2Asqrt%28y%5E2%29%2Asqrt%28y%5E2%29 Break up the square root using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29

10%2Asqrt%282%29%2Asqrt%28y%5E2%29%2Asqrt%28y%5E2%29%2Asqrt%28y%5E2%29 Take the square root of the perfect square 100 to get 10

10%2Asqrt%282%29%2Ay%2Ay%2Ay Take the square root of the perfect squares y%5E2 to get y

10%2Asqrt%282%29%2Ay%5E3 Multiply the common terms
10%2Ay%5E3%2Asqrt%282%29 Rearrange the terms




First let's simplify the numerator

sqrt%285%2Am%5E2%29Start with the numerator

sqrt%285%29%2Asqrt%28m%5E2%29 Break up the square root using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29

sqrt%285%29%2Am Take the square root of the perfect square m%5E2 to get m

m%2Asqrt%285%29 Rearrange the terms


So the expression sqrt%285m%5E2%29%2F2 simplifies to


m%2Asqrt%285%29%2F2