Thread: Find largest square number - without using calculator

Hey All,

This problem must be done without the use of a calculator. I am able to guesstimate my way to a close enough answer but need some help to improve this.

If n is the largest square number such that , find s when

(i)

(ii)

I got (i) easily since its a perfect square,

For (ii) I wrote the number as

Then nearest perfect square close to 10 is 9, so

From there I figured that the number is between and further got to

The problem is that the required answer is and the weight-age is only 1 mark. Using the calculator suggests this is the exactly correct answer.

But since this is a non-calculator use problem, leads me to believe I am missing an obvious/simpler/faster way of getting there. What am I missing?

Thanks again for all your help.

Originally Posted by mathguy80

Hey All,

This problem must be done without the use of a calculator. I am able to guesstimate my way to a close enough answer but need some help to improve this.

If n <-- typo? Shouldn't that be s? is the largest square number such that , find s when

(i)

(ii)

I got (i) easily since its a perfect square,

For (ii) I wrote the number as

Then nearest perfect square close to 10 is 9, so

From there I figured that the number is between and further got to

The problem is that the required answer is and the weight-age is only 1 mark. Using the calculator suggests this is the exactly correct answer.

But since this is a non-calculator use problem, leads me to believe I am missing an obvious/simpler/faster way of getting there. What am I missing?

Thanks again for all your help.

I'm only guessing:



So (see attachment)

Use linear interpolation. According to my sketch

Since you multiply the apprximate value of a by 100 to get s you only have to calculate the first two digits of

Thus

Awesome @earboth! A much clearer and very elegant solution. Learning something new everyday here. Thanks again!