Question

can anybody explain how to solve this?

Answer 1

@RH What exactly does N represent?

Answer 2

I don't know :(

Answer 3

Never mind that, do it normally:\[\bf \sqrt[4]{529}=(529)^{\frac{1}{4}}=(529^{\frac{1}{2}})^{\frac{1}{2}}=(23)^{\frac{1}{2}}\]Now note that square root of 25 is 5 and square root of 16 is 4 so the square will be in the form 4.xx but it will be closer to 5. A nice way (Which I independently discovered) of estimating square roots is to see how far away is 23 from the perfect squares it's contained within. Here 23 lies with the perfect squares 16 and 25 and 7 away from 16 and the different between 16 and 25 is 9. Hence 23 is 7/9 of the way between 16 and 25. Using this information we can estimate the square root by saying that \(\bf \sqrt{23}=4+\frac{7}{9}\). Using long division for 7/9 to get an approximate \(\bf 0.78\) hence \(\bf \sqrt{23} \approx 4.78\). Now look this up in the choices and we see that the closest one to our estimate is a.) and that should be your answer.

Also know that \(\bf \sqrt{23}=4.7958\) approximately which is extremely close to our approximation. I came up with this method of estimating square roots at the end of math class, just before lunch in grade 10 lol =]. And as you can see, it's rather helpful ;].

@RH

Answer 4

Great method! Thank you so much! it's very helpful :)!!!