Grades 9-10 Video Solutions 2013-Level 9&10 Video Solutions 2013 problem10

Video Transcription

Question number 10, which of the following has the largest value?  We note that each expression given to us involves a square root.  We can square each quantity  and then order the resulting integers much faster and easier than we can work with the square root.  However, remembering that the square root is always increasing, the ordering would be preserved after squaring.  So let's do that. Let's square each quantity and compare.  From A we get 20 times 13.  20 times 13 squared from B is already larger.  20 squared times 13 from C is bigger still.  Then from D we have 201 times 9 after squaring and 2013 from E.  Now clearly 2013 is bigger than 201 times 9, which would roughly come out to 1,809.  And so then we have to compare the largest number here, 2013 versus 20 times, 20 times 13.  But 20 squared times 13 is equal to 20 squared or 400 times 13,  which would come out to at least 4,000.  And that is bigger than 2013. And so we conclude that the largest value is 20 times the square root of 13 or answer C.

Video Summary

To determine which expression has the largest value, we can square each one to simplify the comparison, as the square root preserves order. After squaring, we calculate: <br /><br />- From A, we get 20 times 13.<br />- From B, we have 20 squared times 13, which is 400 times 13, equating to over 4,000.<br />- From C, this value is larger than any other calculated expression.<br />- From D, 201 times 9 is approximately 1,809, which is smaller.<br />- From E, the result is 2013, which is also smaller than 4,000.<br /><br />Thus, the largest value corresponds to option C, 20 times the square root of 13.

Keywords

expression comparison

square root

largest value

mathematical calculation

option C