How do you simplify #sqrt(8x^5)* sqrt(10x^3)#?

3 Answers
Alan P.
Jun 27, 2018

#sqrt(8x^5) * sqrt(10x^3)=color(blue)(4sqrt(5)x^4)#

Explanation:

#sqrt(8x^5) * sqrt(10x^3)#

#color(white)("XXX")=sqrt(8 * 10 * x^5 * x^3)#

#color(white)("XXX")=sqrt( 80 * x^8)#

#color(white)("XXX")=sqrt(4^2 * 5 * (x^4)^2)#

#color(white)("XXX")=4sqrt(5)x^4#

Binayaka C.
Jun 27, 2018

# 4 sqrt 5 x^4 #

Explanation:

# sqrt (8 x^5) * sqrt (10 x^3) #

#= sqrt (8 x^5*10 x^3) #

#= sqrt (80 x^8)#

#= sqrt ((4 x^4)^2*5)#

#= 4 sqrt 5 x^4 # [Ans]

Barney V.
Jun 27, 2018

#4 sqrt 5 x^4#

Explanation:

# sqrt (8 x^5)* sqrt (10 x^3)#

#:.8^(1/2)* (x^5)^(1/2)* 10^(1/2)*(x^3)^(1/2)#

#:.2^(1/2)*2^(1/2)*2^(1/2)*x^(5/2)*2^(1/2)*5^(1/2)*x^(3/2)#

#:.2^(4/2)*x^(8/2)*5^(1/2)#

#:.2^2*x^4*sqrt 5#

#:.4 sqrt 5 x^4#

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