SOLUTION: what is the square root of 7x to the 7 times square root of 35x

Question 664934: what is the square root of 7x to the 7 times square root of 35x

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
sqrt(7*x^7 * sqrt(35*x) is equal to sqrt(7*x^7 * 35*x)
since 35x is equivalent to 7*5*x, this expression becomes sqrt(7*x^7*7*5*x)
since x^7*x = x^8, this expression becomes sqrt(7*x^8*7*5)
since 7*7 = 7^2, this expression becomes sqrt(7^2*x^8*5)
since sqrt(7^2) = 7, this expression becomes 7*sqrt(x^8*5)
since x^8 is equal to x^2*x^2*x^2*x^2, this expression becomes 7*sqrt(x^2*x^2*x^2*x^2*5)
since sqrt(x^2) = x, this expression becomes 7*x*x*x*x*sqrt(5)
since x*x*x*x = x^4, this expression becomes 7*x^4*sqrt(5)
that's your answer.
to prove you did good, take any random value of xc and replace x with that value in both the original expression and the final expression to see if both expressions give you the same answer.
the original expression is sqrt(7*x^7) * sqrt(35*x)
replace x with 5
you will need your calculator to solve this.
the original expression becomes sqrt(7*5^7) * sqrt(35*5)
solve this expression using your calculator to get 9782.797402
the final expression is 7*x^4*sqrt(5)
replace x with 5
the final expression becomes 7*5^4*sqrt(5)
solve this expression using your calculator to get 9782.797402
you get the same answer using the original expression and using the final expression which is a good indication that your solution is good.
the final expression is 7*5^4*sqrt(5) which can't be simplified any further.
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