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Which option explains why (\sqrt{p}) is irrational when (p) is a prime number?कौन सा विकल्प बताता है कि (\sqrt{p}) अपरिमेय है जब (p) अभाज्य संख्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Because (p) has no square factor except (1)क्योंकि (p) का कोई वर्ग गुणनखंड (1) के अलावा नहीं होता
Step 1: A prime number (p) is not a perfect square. Step 2: If it is not a perfect square then (\sqrt{p}) cannot be rational. Step 3: Assuming the square root of a prime to be rational leads to a factor contradiction.चरण 1: अभाज्य संख्या (p) पूर्ण वर्ग नहीं होती। चरण 2: पूर्ण वर्ग न होने पर (\sqrt{p}) परिमेय नहीं हो सकता। चरण 3: अभाज्य संख्या के वर्गमूल को परिमेय मानने से गुणनखंडों में विरोधाभास आता है।
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