Add 321−−√ + 721−−√ .(1 point) Responses 1021−−√ 10 Start Root 21 End Root 52−−√ Start Root 52 End Root 1042−−√ 10 Start Root 42 End Root 24 −−−√ + 28−−√
The simplified expression for 321√ + 721√ is 10√21 + 8√2.
Add 19−−√ + 19−−√ .(1 point) Responses 219−−√ 2 Start Root 19 End Root 238−−√ 2 Start Root 38 End Root 20−−√ Start Root 20 End Root 40−−√
The simplified expression for 19√ + 19√ is 2√19 + 2√19, which can be further simplified to 4√19.
Add 22−−√3 + 322−−√ + 22−−√ .(1 point) Responses 22−−√3 + 422−−√ root index 3 Start Root 22 End Root plus 4 Start Root 22 End Root 522−−√ 5 Start Root 22 End Root 566−−√ 5 Start Root 66 End Root 22−−√3 + 444−−√ root index 3 Start Root 22 End Root plus 4 Start Root 44 End Root
The simplified expression for √3 + 32√ + √2 is √3 + 4√2 + √2, which can be further simplified to √3 + 5√2.
Please note that there is an error in the provided responses, as the expression is 22√3 + 32√ + 22√, not 22√3 + 422√ or 22√3 + 444√.
To solve the expression 321−−√ + 721−−√, we need to simplify each square root term individually.
Let's start with the first term, √321.
To simplify a square root, we look for perfect square factors of the radicand (the number inside the square root).
In this case, we can see that 16 is a perfect square that divides 321 (16 x 20 = 320). So we can rewrite √321 as √(16 x 20).
Now we can break down the square root using the product property: √(ab) = √a x √b.
The square root of 16 is 4, and the square root of 20 cannot be simplified further. Therefore, √(16 x 20) can be simplified to 4√20.
Moving on to the second term, √721.
Similar to the previous step, we look for perfect square factors of 721. We can see that 25 is a perfect square that divides 721 (25 x 29 = 725). So we can rewrite √721 as √(25 x 29).
Using the product property, we can break down the square root: √(25 x 29) = √25 x √29.
The square root of 25 is 5, and the square root of 29 cannot be simplified further. Therefore, √(25 x 29) can be simplified to 5√29.
Now we can rewrite the original expression as 4√20 + 5√29.
Since there are no like terms, we cannot combine the square roots any further. Thus, the simplified expression is 4√20 + 5√29.