Add and Subtract Radicals Quick Check
Math 8 Q2 (Pre-Algebra) / Roots and Irrational Numbers
add 2 square root 21 + 3 square root 21
10 square root 21
10 square root 42
square root 52
square root 24 + square root 28
what is the answer
The answer is square root 52.
To add or subtract radicals, you can only combine terms that have the same radical expression.
In the first problem, you are asked to simplify: 2√21 + 3√21.
Since both terms have the same radical expression (√21), you can combine them.
2√21 + 3√21 = (2 + 3)√21 = 5√21.
Therefore, the answer is 5√21.
In the second problem, you are asked to simplify: √24 + √28.
Unfortunately, the terms √24 and √28 do not have the same radical expression, so they cannot be combined directly.
However, you can simplify each term individually by finding perfect square factors.
√24 can be simplified as √(4 * 6) = √4 * √6 = 2√6.
√28 can be simplified as √(4 * 7) = √4 * √7 = 2√7.
Therefore, the simplified expression is: 2√6 + 2√7.
Note: It is not possible to further simplify 2√6 + 2√7 since the terms have different radical expressions.
To add or subtract radicals, you need to make sure you are combining like terms. In this case, both terms have the same radical, which is the square root of 21. To add or subtract these terms, simply combine the coefficients (numbers in front of the radical) and keep the radical the same.
So, for the first expression:
2√21 + 3√21 = (2 + 3)√21 = 5√21
Therefore, the answer to "2 square root 21 + 3 square root 21" is "5 square root 21."
For the second expression:
√24 + √28, you need to simplify the radicals before combining them. Start by factoring the numbers inside the radicals:
√24 = √(4 * 6) = 2√6
√28 = √(4 * 7) = 2√7
Now, add the simplified radicals:
2√6 + 2√7 = 2(√6 + √7)
The answer to "square root 24 + square root 28" is "2 times the square root of 6 plus the square root of 7."