Question

Please can someone show me how to work this out step by step without a calculator

Answer 1

$2\sqrt8\times8\sqrt2=(2\times8)\sqrt{8\times2}=16\sqrt{16}=16\times4=64$

Alternatively, you can write radicals as rational exponents, so that you get

$2\sqrt8\times8\sqrt2=2\tiems8^{1/2}\times8\times2^{1/2}=2^{3/2}8^{3/2}$

Then recalling that $2^3=8$, you have

$2^{3/2}8^{3/2}=2^{3/2}(2^3)^{3/2}=2^{3/2}2^{9/2}=2^{12/2}=2^6=64$