Here are the step-by-step solutions for each problem on the worksheet.
1) $3\sqrt{6} - 4\sqrt{6}$
* These are like terms because they both have $\sqrt{6}$.
* Subtract the numbers in front: $3 - 4 = -1$.
*
Answer: $-\sqrt{6}$
2) $-3\sqrt{7} + 4\sqrt{7}$
* These are like terms ($\sqrt{7}$).
* Add the numbers in front: $-3 + 4 = 1$.
*
Answer: $\sqrt{7}$
3) $-11\sqrt{21} - 11\sqrt{21}$
* Like terms ($\sqrt{21}$).
* Subtract: $-11 - 11 = -22$.
*
Answer: $-22\sqrt{21}$
4) $-9\sqrt{15} + 10\sqrt{15}$
* Like terms ($\sqrt{15}$).
* Add: $-9 + 10 = 1$.
*
Answer: $\sqrt{15}$
5) $-10\sqrt{7} + 12\sqrt{7}$
* Like terms ($\sqrt{7}$).
* Add: $-10 + 12 = 2$.
*
Answer: $2\sqrt{7}$
6) $-3\sqrt{17} - 4\sqrt{17}$
* Like terms ($\sqrt{17}$).
* Subtract: $-3 - 4 = -7$.
*
Answer: $-7\sqrt{17}$
7) $-10\sqrt{11} - 11\sqrt{11}$
* Like terms ($\sqrt{11}$).
* Subtract: $-10 - 11 = -21$.
*
Answer: $-21\sqrt{11}$
8) $-2\sqrt{3} + 3\sqrt{27}$
* First, simplify $\sqrt{27}$. Since $27 = 9 \times 3$, then $\sqrt{27} = \sqrt{9}\cdot\sqrt{3} = 3\sqrt{3}$.
* Multiply by the 3 in front: $3(3\sqrt{3}) = 9\sqrt{3}$.
* Now the problem is: $-2\sqrt{3} + 9\sqrt{3}$.
* Add: $-2 + 9 = 7$.
*
Answer: $7\sqrt{3}$
9) $2\sqrt{6} - 2\sqrt{24}$
* First, simplify $\sqrt{24}$. Since $24 = 4 \times 6$, then $\sqrt{24} = \sqrt{4}\cdot\sqrt{6} = 2\sqrt{6}$.
* Multiply by the 2 in front: $2(2\sqrt{6}) = 4\sqrt{6}$.
* Now the problem is: $2\sqrt{6} - 4\sqrt{6}$.
* Subtract: $2 - 4 = -2$.
*
Answer: $-2\sqrt{6}$
10) $2\sqrt{6} + 3\sqrt{54}$
* First, simplify $\sqrt{54}$. Since $54 = 9 \times 6$, then $\sqrt{54} = \sqrt{9}\cdot\sqrt{6} = 3\sqrt{6}$.
* Multiply by the 3 in front: $3(3\sqrt{6}) = 9\sqrt{6}$.
* Now the problem is: $2\sqrt{6} + 9\sqrt{6}$.
* Add: $2 + 9 = 11$.
*
Answer: $11\sqrt{6}$
11) $-\sqrt{12} + 3\sqrt{3}$
* First, simplify $\sqrt{12}$. Since $12 = 4 \times 3$, then $\sqrt{12} = \sqrt{4}\cdot\sqrt{3} = 2\sqrt{3}$.
* So, $-\sqrt{12}$ becomes $-2\sqrt{3}$.
* Now the problem is: $-2\sqrt{3} + 3\sqrt{3}$.
* Add: $-2 + 3 = 1$.
*
Answer: $\sqrt{3}$
12) $3\sqrt{3} - \sqrt{27}$
* First, simplify $\sqrt{27}$. Since $27 = 9 \times 3$, then $\sqrt{27} = 3\sqrt{3}$.
* Now the problem is: $3\sqrt{3} - 3\sqrt{3}$.
* Subtract: $3 - 3 = 0$.
*
Answer: $0$
Final Answer:
1) $-\sqrt{6}$
2) $\sqrt{7}$
3) $-22\sqrt{21}$
4) $\sqrt{15}$
5) $2\sqrt{7}$
6) $-7\sqrt{17}$
7) $-21\sqrt{11}$
8) $7\sqrt{3}$
9) $-2\sqrt{6}$
10) $11\sqrt{6}$
11) $\sqrt{3}$
12) $0$
Parent Tip: Review the logic above to help your child master the concept of adding and subtracting radical expressions worksheet answers.
