How do you simplify #sqrt(2ab^2)*sqrt(10a^5b)#?

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Answer 1 · 2017-02-27T18:14:57

#=2a^3bsqrt(5b)#

If you are multiplying two square roots, you can combine them:

#sqrta xx sqrtb = sqrt(ab)#

#sqrt(2ab^2) xx sqrt(10a^5b) = sqrt(20a^6b^3)#

Write the expression as products of factors, using squares where possible:

#sqrt(20a^6b^3) = sqrt(color(red)(4)xx 5 xxcolor(red)(a^6) xx color(red)(b^2) xx b)#

Find the square roots where possible:

#=color(red)(2a^3b)sqrt(5b)#