It looks like you've uploaded a worksheet titled
"Addition and Subtraction of Square Roots", which contains a series of problems involving the addition and subtraction of square roots. Since I can't view images directly, I'll guide you through how to solve these types of problems and provide a general explanation.
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🔧 How to Add and Subtract Square Roots
You can only add or subtract square roots if they are
like terms — that is, if they have the
same radicand (the number under the square root).
For example:
- $ \sqrt{2} + 3\sqrt{2} = 4\sqrt{2} $
- $ 5\sqrt{3} - 2\sqrt{3} = 3\sqrt{3} $
But:
- $ \sqrt{2} + \sqrt{3} $
cannot be simplified further because the radicands are different.
Sometimes, you may need to
simplify the square roots first before combining them.
#### Example:
Simplify $ \sqrt{8} + \sqrt{18} $
1. Simplify each radical:
- $ \sqrt{8} = \sqrt{4 \cdot 2} = 2\sqrt{2} $
- $ \sqrt{18} = \sqrt{9 \cdot 2} = 3\sqrt{2} $
2. Now add:
- $ 2\sqrt{2} + 3\sqrt{2} = 5\sqrt{2} $
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✔ General Steps:
1.
Simplify each square root by factoring out perfect squares.
2.
Combine like terms (same radicands).
3.
Leave unlike radicals as they are.
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📝 Let’s Solve a Few Sample Problems from Your Worksheet
Since I can’t see your image, here are common types of problems found on such worksheets:
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#### Problem 1: $ \sqrt{12} + \sqrt{27} $
- $ \sqrt{12} = \sqrt{4 \cdot 3} = 2\sqrt{3} $
- $ \sqrt{27} = \sqrt{9 \cdot 3} = 3\sqrt{3} $
- $ 2\sqrt{3} + 3\sqrt{3} = 5\sqrt{3} $
✔ Answer: $ 5\sqrt{3} $
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#### Problem 2: $ 4\sqrt{5} - \sqrt{20} $
- $ \sqrt{20} = \sqrt{4 \cdot 5} = 2\sqrt{5} $
- $ 4\sqrt{5} - 2\sqrt{5} = 2\sqrt{5} $
✔ Answer: $ 2\sqrt{5} $
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#### Problem 3: $ \sqrt{50} + \sqrt{18} - \sqrt{8} $
- $ \sqrt{50} = \sqrt{25 \cdot 2} = 5\sqrt{2} $
- $ \sqrt{18} = \sqrt{9 \cdot 2} = 3\sqrt{2} $
- $ \sqrt{8} = \sqrt{4 \cdot 2} = 2\sqrt{2} $
- $ 5\sqrt{2} + 3\sqrt{2} - 2\sqrt{2} = 6\sqrt{2} $
✔ Answer: $ 6\sqrt{2} $
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#### Problem 4: $ \sqrt{12} - \sqrt{3} $
- $ \sqrt{12} = 2\sqrt{3} $
- $ 2\sqrt{3} - \sqrt{3} = \sqrt{3} $
✔ Answer: $ \sqrt{3} $
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✘ Common Mistake:
Do
not combine unlike radicals:
- $ \sqrt{2} + \sqrt{3} $ stays as $ \sqrt{2} + \sqrt{3} $
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📌 Tips:
- Always simplify radicals first.
- Only combine terms with the same radical.
- Write answers in simplest form.
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If you can
type out a few specific problems from the worksheet, I’ll solve them step-by-step for you!
Let me know!
Parent Tip: Review the logic above to help your child master the concept of adding square roots worksheet.
