Question

Which is the MOST reasonable estimate for "the square root of eight divided by two to the second power?

Answer 1

We want to estimate:

`(√(8) )/(2^2)`

We can rewrite this as:

`(√(8) )/(2^2) = (√(8) )/(4) =(√(8) )/(√(4^2) ) =\sqrt{(8)/(4*4) } = \sqrt{(2)/(4) } = (1)/(√(2) )`

And √2 is a notable value, we know that:

√2 ≈ 1.41

Then:

`(1)/(√(2) ) = (1)/(1.41) = 0.7`

then:

`(√(8) )/(2^2) = 0.7`

is a really good estimation.

if instead:

"the square root of eight divided by two to the second power"

refers to:

`\sqrt{(8)/(2^2) }`

is easier, we just can replace 2^2 = 4, then we get:

`\sqrt{(8)/(2^2) } = \sqrt{(8)/(4) } = √(2) = 1.41`

Is also a really good aproximation.