[tex]\sqrt{2 \cdot 3}[/tex]
Answer (2)
Multiply the numbers inside the square root: 2 ⋅ 3 = 6 .
Simplify the expression to 6 .
Since 6 has no perfect square factors other than 1, the expression is already in simplest form.
The simplified expression is 6 .
Explanation
Understanding the problem We are given the expression 2 ⋅ 3 and we want to simplify it.
Multiplication First, we perform the multiplication inside the square root: 2 ⋅ 3 = 6 .
Simplifying the square root So, the expression becomes 6 . Since 6 does not have any perfect square factors other than 1 (i.e., 6 is not divisible by 4, 9, 16, etc.), the square root of 6 is already in its simplest form.
Final Answer Therefore, the simplified expression is 6 .
Examples
Square roots are used in many areas of math and science. For example, when calculating the distance between two points in a plane, you use the distance formula, which involves square roots. If you have two points (1, 2) and (4, 6), the distance between them is ( 4 − 1 ) 2 + ( 6 − 2 ) 2 = 3 2 + 4 2 = 9 + 16 = 25 = 5 . Square roots are also used in physics to calculate things like the speed of an object or the period of a pendulum.
To simplify 2 ⋅ 3 , first multiply the numbers to get 6 and then rewrite it as 6 . Since 6 has no perfect square factors other than 1, the expression is already in its simplest form. Thus, the final answer is 6 .
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