The square of 6 less than a number is 784. In the positive case, what is the number?
Answer and explanation
Correct answer: 34
Let the number be x. The phrase “6 less than the number” means x − 6, so the statement becomes (x − 6)² = 784. Since 784 = 28², taking square roots gives x − 6 = ±28. Thus the two algebraic possibilities are x = 34 and x = −22. The question asks for the positive case, so x = 34 must be selected. Substitution confirms it: (34 − 6)² = 28² = 784. Option A, 28, is only the positive square-root value and is not the original number; 30 and 36 do not satisfy the equation. Therefore option C is the unique correct answer.
Frequently asked questions
What is the correct answer to this question?
34
Why is this the correct answer?
Let the number be x. The phrase “6 less than the number” means x − 6, so the statement becomes (x − 6)² = 784. Since 784 = 28², taking square roots gives x − 6 = ±28. Thus the two algebraic possibilities are x = 34 and x = −22. The question asks for the positive case, so x = 34 must be selected. Substitution confirms it: (34 − 6)² = 28² = 784. Option A, 28, is only the positive square-root value and is not the original number; 30 and 36 do not satisfy the equation. Therefore option C is the unique correct answer.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Word Problems and Applications.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
