If x = √5 + √3, then what type of number is x²?
Answer and explanation
Correct answer: 8 + 2√15, irrational
Apply the square-of-a-sum identity to the given surds: x² = (√5 + √3)² = 5 + 2√15 + 3 = 8 + 2√15. The number √15 is irrational, and multiplying it by the nonzero rational number 2 remains irrational. Adding the rational number 8 also gives an irrational number; otherwise √15 would become rational after subtracting 8 and dividing by 2. Thus option A is correct. Option B is only the sum of the individual squares and omits the cross term. Option C incorrectly multiplies 5 and 3, while option D is not equal to the expansion. The cross term determines the result.
Frequently asked questions
What is the correct answer to this question?
8 + 2√15, irrational
Why is this the correct answer?
Apply the square-of-a-sum identity to the given surds: x² = (√5 + √3)² = 5 + 2√15 + 3 = 8 + 2√15. The number √15 is irrational, and multiplying it by the nonzero rational number 2 remains irrational. Adding the rational number 8 also gives an irrational number; otherwise √15 would become rational after subtracting 8 and dividing by 2. Thus option A is correct. Option B is only the sum of the individual squares and omits the cross term. Option C incorrectly multiplies 5 and 3, while option D is not equal to the expansion. The cross term determines the result.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Irrational numbers and real numbers.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
