Answer:
We want to estimate:
[tex]\frac{\sqrt{8} }{2^2}[/tex]
We can rewrite this as:
[tex]\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} }[/tex]
And √2 is a notable value, we know that:
√2 ≈ 1.41
Then:
[tex]\frac{1}{\sqrt{2} } = \frac{1}{1.41} = 0.7[/tex]
then:
[tex]\frac{\sqrt{8} }{2^2} = 0.7[/tex]
is a really good estimation.
if instead:
"the square root of eight divided by two to the second power"
refers to:
[tex]\sqrt{\frac{8}{2^2} }[/tex]
is easier, we just can replace 2^2 = 4, then we get:
[tex]\sqrt{\frac{8}{2^2} } = \sqrt{\frac{8}{4} } = \sqrt{2} = 1.41[/tex]
Is also a really good aproximation.
