Question Video: Finding the Closest Value to the Sum of Numbers with Integer Powers Mathematics

Which of the following is closest to 7² + 11²? [A] 14 + 22 [B] 18² [C] 27 + 211 [D] 49 + 11 [E] 49 + 119?


Video Transcript

Which of the following is closest to seven squared plus 11 squared? Is it (A) 14 plus 22, (B) 18 squared, (C) 27 plus 211, (D) 49 plus 11, or (E) 49 plus 119?

When squaring a number, we need to multiply the number by itself. This means that seven squared is equal to seven multiplied by seven. This is equal to 49. 11 squared is equal to 11 multiplied by 11. As 11 multiplied by 10 is 110, 11 multiplied by 11 is 121. The calculation seven squared plus 11 squared is therefore equal to 49 plus 121. This gives a final answer of 170. However, this is not one of our five options. The answer that is closest to 49 plus 121 is option (E) 49 plus 119.

Option (A) is incorrect, as the numbers have been multiplied by two and not squared. Seven multiplied by two is 14, and 11 multiplied by two is 22. In option (B), the numbers seven and 11 have been added before squaring. This is incorrect. In option (C), neither of the values are correct and the total answer is 238. In option (D), the first part seven squared is correct. However, the 11 has not been squared. This means that option (D) is incorrect, giving us the correct answer option (E).

49 plus 119 which is equal to 168 is closest to seven squared plus 11 squared, which is 170.

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