How do you simplify #sqrt32*sqrt144#?

1 Answer
Ratnaker Mehta
Jul 1, 2016

#48sqrt2.#

Explanation:

We use prime factorisation of #32=2^5# and #144=2^4*3^2.#

Hence the expression, #=sqrt32*sqrt144,#
#=(2^5)^(1/2)*(2^4*3^2)^(1/2)#=#(2^4*2)^(1/2)*(2^4*3^2)^(1/2)#
#={(2^4)^(1/2)2^(1/2)}{(2^4)^(1/2)*(3^2)^(1/2)}#=#2^(4*1/2)*2^(1/2)*2^(4*1/2)*3^(2*1/2)=2^2*2^(1/2)*2^2*3^1=4*sqrt2*4*3=48sqrt2.#

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