Tag Archives: power

Value of Sum

What is the value of the following sum? Source: NCTM Mathematics Teacher, September 2006 Solution The square bracket in the sum expression contains 1003 pairs of consecutive powers which pairwise sum to zero Answer:

Posted in Problem solving | Tagged , , | Leave a comment

2x^2=3y^2

What is the only pair of integers for which twice the square of the first equals three times the square of the second? Source: NCTM Mathematics Teacher, October 2006 Solution We are looking for integers such that . If , … Continue reading

Posted in Problem solving | Tagged , , , , , , , , , , , | Leave a comment

Thirteen Power of (1+i)

If  represents the imaginary unit, find real values for and such that . Source: NCTM Mathematics Teacher, October 2006 Solution Answer: Alternative solution Write the complex number in polar form Applying De Moivre’s theorem

Posted in Problem solving | Tagged , , , , , , | Leave a comment

Exponent Value

What is the integer for which ? Source: NCTM Mathematics Teacher, October 2006 Solution Answer:

Posted in Problem solving | Tagged , , , , | Leave a comment

Volumes of Two Cubes

The combined volumes of two cubes with integer side lengths are numerically equal to the combined lengths of their edges. What are the dimensions of the cubes? Source: NCTM Mathematics Teacher, January 2006 Solution Suppose is the side length of … Continue reading

Posted in Problem solving | Tagged , , , , , , , , | Leave a comment

Perfect Squares and Perfect Cubes

List all integers less than that are both perfect squares and perfect cubes. Source: NCTM Mathematics Teacher, January 2006 Solution is a perfect square but not a perfect cube. On the other hand, is a perfect cube but not a … Continue reading

Posted in Problem solving | Tagged , , , , , , , | Leave a comment

Value of Exponent

What is the value of if ? Source: NCTM Mathematics Teacher, January 2006 SOLUTION Answer:

Posted in Problem solving | Tagged , , , | Leave a comment

Perfect Square

Find the smallest positive integer such that is a perfect square, is a perfect cube, and is a perfect fifth power. Source: NCTM Mathematics Teacher, December 2005 SOLUTION If is a perfect square, must have as a prime factor such … Continue reading

Posted in Problem solving | Tagged , , , , , , , , , , | Leave a comment

Perfect Square

What is the smallest positive integer such that is a perfect square? Source: NCTM Mathematics Teacher, December 2005 SOLUTION will be smallest when we make the numerator as large a perfect square as it can be. Answer:

Posted in Problem solving | Tagged , , , , , , , , | Leave a comment

Sum of Digits

Find the sum of the digits in the expression . Source: NCTM Mathematics Teacher, December 2005 SOLUTION If we multiply the numbers by hand, we have the following addition ———————————- The sum of the digits equals . Answer: Alternative solution … Continue reading

Posted in Uncategorized | Tagged , , , , , , , | Leave a comment