{"id":26029,"date":"2025-06-19T09:27:52","date_gmt":"2025-06-19T09:27:52","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=26029"},"modified":"2025-06-19T09:27:55","modified_gmt":"2025-06-19T09:27:55","slug":"the-product-of-square-root-2-and-square-root-50-is-rational-or-irrational","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/the-product-of-square-root-2-and-square-root-50-is-rational-or-irrational\/","title":{"rendered":"The product of square root 2 and square root 50 is rational or irrational"},"content":{"rendered":"\n

The product of square root 2 and square root 50 is rational or irrational<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Correct Answer: The product of \u221a2 and \u221a50 is irrational.<\/strong><\/p>\n\n\n\n

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Explanation:<\/strong><\/p>\n\n\n\n

To determine whether the product of \u221a2 and \u221a50 is rational or irrational, we first simplify the expression:2\u00d750\\sqrt{2} \\times \\sqrt{50}2\u200b\u00d750\u200b<\/p>\n\n\n\n

Using the property of square roots:a\u00d7b=ab\\sqrt{a} \\times \\sqrt{b} = \\sqrt{ab}a\u200b\u00d7b\u200b=ab\u200b<\/p>\n\n\n\n

We get:2\u00d750=100\\sqrt{2 \\times 50} = \\sqrt{100}2\u00d750\u200b=100\u200b100=10\\sqrt{100} = 10100\u200b=10<\/p>\n\n\n\n

This result, 10, is a rational number<\/strong> because it can be expressed as a fraction (10\/1), which meets the definition of a rational number: any number that can be written as a ratio of two integers where the denominator is not zero.<\/p>\n\n\n\n

So, while \u221a2 and \u221a50 are both irrational numbers individually<\/strong>, their product simplifies in this specific case to a rational number. This is not typical of irrational numbers \u2014 usually, multiplying two irrational numbers results in another irrational number. But there are exceptions, like this one.<\/p>\n\n\n\n

Let\u2019s break it down further:<\/p>\n\n\n\n