Question

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

Answer 1

`2\sqrt8*8\sqrt2=(2*8)√(8*2)=16√(16)=16*4=64`

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


`2\sqrt8*8\sqrt2=2\tiems8^(1/2)*8*2^(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`