Usually when working with big numbers like this, it is more efficient to use a calculator. You could easily find online calculators to help you.

Using a calculator, the square root of 37,932,330 would indeed round to 6159 (rounded to the nearest whole number).

Yes I understand. The problem being is the part in the question that says "show your work". I would have to say calculators are not allowed in the test.

Calulators are allowed in some tests; some of the math cannot be easily done by hand, and so the calulators are there to use when there are problems like "Solve the right triangle" and you need to know what sin63 is.

I'm pretty sure a calculator would be allowed to be used when dealing with that type of problem. For the showing your work part, the students can show the problem they typed in their calculator. For example, the student can type in sin(63) in their calculator and to show their work, they could write sin(63)=0.89 (rounded to the nearest hundredth).

Hope this helps.

This problem is at a grade 8 level, triganomity is mot taught till high school. Just wish I could see a video where this is explained in detail.

Here, this might help then.

https://www.khanacademy.org/math/algebra/rational-exponents-and-radicals/alg1-simplify-square-roots/a/simplifying-square-roots-review

That was an interesting link, however simplifying a 2 digit root is not really helpful when the number is in the millions and calculators are not allowed to be used. 

I'm sorry that I could not have been more of assistance to you, but my whole point of all of this is that 8th graders are not really expected to solve the square roots of really high numbers, and because of that, I recommend just using the calculator. If you insist on showing your work, then you could simplying that square root, just like how you would simplify a two digit square root, lay out all the factors and simplify. It would take an awfully long time though.

Good day!

Perhaps the problem may be that we live in Canada where the level of math required for grade 8 students is higher than where you may be currently residing. The text book is published by Nelson called mathematics 8 student workbook #0-17-626996-7.