{"id":271349,"date":"2025-07-25T17:55:54","date_gmt":"2025-07-25T17:55:54","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=271349"},"modified":"2025-07-25T17:55:56","modified_gmt":"2025-07-25T17:55:56","slug":"what-are-the-positive-and-negative-square-roots-of-64-25","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/25\/what-are-the-positive-and-negative-square-roots-of-64-25\/","title":{"rendered":"What are the positive and negative square roots of 64\/25"},"content":{"rendered":"\n

What are the positive and negative square roots of 64\/25<\/p>\n\n\n\n

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

The square roots of a number xxx are the values that, when multiplied by themselves, give xxx. The square roots of a number always have two values: one positive and one negative.<\/p>\n\n\n\n

For the number 6425\\frac{64}{25}2564\u200b, we can find the square roots by first taking the square root of the numerator (64) and the denominator (25) separately, and then combining the results. 6425=6425=85\\sqrt{\\frac{64}{25}} = \\frac{\\sqrt{64}}{\\sqrt{25}} = \\frac{8}{5}2564\u200b\u200b=25\u200b64\u200b\u200b=58\u200b<\/p>\n\n\n\n

The square root of 646464 is 8, and the square root of 252525 is 5. Therefore, the principal (positive) square root of 6425\\frac{64}{25}2564\u200b is 85\\frac{8}{5}58\u200b.<\/p>\n\n\n\n

However, for any positive number xxx, there are always two square roots: one positive and one negative. Therefore, the square roots of 6425\\frac{64}{25}2564\u200b are: \u00b185\\pm \\frac{8}{5}\u00b158\u200b<\/p>\n\n\n\n

This means that both 85\\frac{8}{5}58\u200b and \u221285-\\frac{8}{5}\u221258\u200b are square roots of 6425\\frac{64}{25}2564\u200b.<\/p>\n\n\n\n

Explanation:<\/h3>\n\n\n\n

The square root function has two outputs for any positive input because both positive and negative numbers, when squared, give the same result. For example:<\/p>\n\n\n\n