{"id":280516,"date":"2025-08-04T20:16:13","date_gmt":"2025-08-04T20:16:13","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=280516"},"modified":"2025-08-04T20:16:16","modified_gmt":"2025-08-04T20:16:16","slug":"which-of-the-following-expressions-are-equivalent-to-sqrt48","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/08\/04\/which-of-the-following-expressions-are-equivalent-to-sqrt48\/","title":{"rendered":"Which of the following expressions are equivalent to sqrt(48)\u00a0"},"content":{"rendered":"\n
\"\"<\/figure>\n\n\n\n

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

The correct answers are B and C.<\/p>\n\n\n\n

To determine which expressions are equivalent to the square root of 48 (\u221a48), we should first simplify \u221a48 and then evaluate each option to see if it matches.<\/p>\n\n\n\n

The process of simplifying a square root involves finding the largest perfect square that is a factor of the number under the radical sign. A perfect square is the product of an integer with itself, like 4 (2×2), 9 (3×3), or 16 (4×4).<\/p>\n\n\n\n

Let’s find the factors of 48 to identify the largest perfect square factor:
The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
The perfect squares in this list are 4 and 16. The largest one is 16.<\/p>\n\n\n\n

Now, we can rewrite \u221a48 as the square root of the product of 16 and 3:
\u221a48 = \u221a(16 \u00d7 3)<\/p>\n\n\n\n

Using the property of radicals which states that \u221a(a \u00d7 b) = \u221aa \u00d7 \u221ab, we can separate the terms:
\u221a(16 \u00d7 3) = \u221a16 \u00d7 \u221a3<\/p>\n\n\n\n

Since the square root of 16 is 4, the simplified expression is:
4\u221a3<\/p>\n\n\n\n

This shows that Option C, 4\u221a3, is equivalent to \u221a48.<\/p>\n\n\n\n

The question asks us to select all expressions that apply, so we must check every option. We can verify each choice by converting it into a single radical of the form \u221ax. This is done by squaring the coefficient (the number outside the radical) and multiplying it by the number inside the radical.<\/p>\n\n\n\n