How do you multiply #\sqrt { 2b ^ { 6} } \sqrt { 10b ^ { 4} }#?

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Answer 1 · 2018-01-18T06:28:15

#sqrt(20b^10# which can be simplified to #2b^5sqrt5#

#sqrt(2b^6# *#sqrt(10b^4#=#sqrt(2b^6*10b^4#=#sqrt(20b^(6+4#=#sqrt(20b^10#
This could be simplified to #2b^5sqrt5#

Answer 2 · 2018-01-18T06:48:13

#sqrt(2b^6)*sqrt(10b^4)=color(blue)(2b^5sqrt(5)#

Refer to the explanation for the process.

Multiply:

#sqrt(2b^6)*sqrt(10b^4)#

Apply rule: #sqrt(ab)=sqrtasqrtb#

#sqrt2sqrt(b^6)*sqrt(10b^4)#

Simplify #sqrt(b^6)# to #b^3#.

#b^3sqrt2sqrt(10b^4)#

Apply rule: #sqrt(ab)=sqrtasqrtb#

#b^3sqrt2sqrt(10)sqrt(b^4)#

Simplify #sqrt(b^4)# to #b^2#.

#b^2sqrt2b^2sqrt10#

Apply rule: #sqrtasqrtb=sqrt(ab)#

#sqrt2sqrt10b^3b^2=sqrt(20)b^3b^2#

Prime factorize #20#.

#sqrt(2xx2xx5)b^3b^2#

Simplify.

#2sqrt(5)b^3b^2#

Apply rule: #a^ma^n=a^(m+n)#.

#2sqrt(5)b^(3+2)#

Simplify.

#2sqrt(5)b^5#

Simplify.

#2b^5sqrt(5)#