Question

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

Answer 1

Answer:

We want to estimate:

$\frac{\sqrt{8} }{2^2}$

We can rewrite this as:

$\frac{\sqrt{8} }{2^2} = \frac{\sqrt{8} }{4} =\frac{\sqrt{8} }{\sqrt{4^2} } =\sqrt{\frac{8}{4*4} } = \sqrt{\frac{2}{4} } = \frac{1}{\sqrt{2} }$

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

√2 ≈ 1.41

Then:

$\frac{1}{\sqrt{2} } = \frac{1}{1.41} = 0.7$

then:

$\frac{\sqrt{8} }{2^2} = 0.7$

is a really good estimation.

if instead:

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

refers to:

$\sqrt{\frac{8}{2^2} }$

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

$\sqrt{\frac{8}{2^2} } = \sqrt{\frac{8}{4} } = \sqrt{2} = 1.41$

Is also a really good aproximation.