$7 \sqrt{5}+4 \sqrt{5}$

Identify the common radical term: 5 ​ .
Factor out the common term: ( 7 + 4 ) 5 ​ .
Add the coefficients: 7 + 4 = 11 .
State the final simplified expression: 11 5 ​ ​ .

Explanation

Analyzing the Expression We are asked to simplify the expression 7 5 ​ + 4 5 ​ . Notice that both terms contain the same radical, which is 5 ​ . This allows us to combine these terms easily.

Factoring and Simplifying To simplify the expression, we can factor out the common term 5 ​ from both terms:


7 5 ​ + 4 5 ​ = ( 7 + 4 ) 5 ​ Now, we simply add the numbers inside the parenthesis: 7 + 4 = 11 .

Final Result Therefore, the simplified expression is:

( 7 + 4 ) 5 ​ = 11 5 ​
So, the final simplified expression is 11 5 ​ .
Examples
Imagine you are calculating the total length of two pieces of wood needed for a project. If one piece is 7 5 ​ inches long and the other is 4 5 ​ inches long, adding them together gives you the total length needed, which is 11 5 ​ inches. This kind of calculation is useful in various fields like construction, engineering, and even cooking when dealing with specific proportions or scaling recipes.

Answered by GinnyAnswer | 2025-07-08

The expression 7 5 ​ + 4 5 ​ simplifies to 11 5 ​ by factoring out the common radical term and adding the coefficients. The common term is 5 ​ , and when combined, the coefficients result in 11. Therefore, the final answer is 11 5 ​ .
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Answered by Anonymous | 2025-08-19