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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