Suma y Resta de Números Radicales.

Simplifying Radical Expressions: A Step-by-Step Guide

Introduction to the Exercise

• The video introduces an exercise involving the addition and subtraction of radical values, specifically focusing on the expression 3sqrt18 - 4sqrt8 + sqrt24.

• The first step is to simplify all radicals present in the exercise, ensuring that simplification is possible.

Simplifying sqrt18

• To simplify sqrt18, it is factored into prime components: 18 = 9 times 2. This reveals a perfect square.

• The simplification results in 3sqrt2 since sqrt9 = 3 and sqrt2 remains under the radical.

Simplifying sqrt8

• For sqrt8, it is broken down as 8 = 4 times 2, identifying another perfect square.

• This leads to a simplified form of 2sqrt2 because sqrt4 = 2. Thus, we express it as two separate radicals: sqrt4 cdot sqrt2.

Simplifying sqrt24

• The value inside the radical for 24 is decomposed into its factors: 24 = 4 times 6. Here, again we find a perfect square.

• This simplifies to 2sqrt6, where we keep both parts separated as before with their respective roots. Thus, we have: 2cdot3 = 6.

Substituting Back into the Expression

• After simplifying each radical, they are substituted back into the original expression:

• Replace 3sqrt18 with 3(3sqrt2) = 9.

• Replace 4sqrt8 with 4(2sqrt2) = 8.

• Keep the term for root of twenty-four as it was simplified earlier.

Final Calculation Steps

• The next step involves performing arithmetic operations on whole numbers and like terms:

• Combine integer values: 9 - 8 + (terms with roots).

• Only like terms can be combined; thus, you get a final result of:

• Resulting integer part becomes 1 + (remaining terms): which includes any unsimplified radicals such as those from previous steps.

Conclusion

• Ultimately, after all calculations and simplifications are done correctly, one arrives at a final expression that may not always need further reduction unless specified by context or additional instructions given in exercises or problems presented later on.

• In this case, it's expressed simply as:

• Final Result:

$$1 + 2√6$$

where typically only significant figures are noted without writing out integers if they equal one unless otherwise stated in mathematical conventions.