Adding and Subtracting Radicals
This worksheet focuses on adding and subtracting radical expressions, including simplifying before combining terms.
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Adding and Subtracting Radicals
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Simplify each radical expression and then add or subtract as indicated. Ensure all answers are in simplest radical form.
1. Simplify and combine: √12 + √27
2. Simplify and combine: 5√8 - 3√18
3. Simplify and combine: √75 + √48 - √3
4. To add or subtract radicals, their (the number under the radical sign) must be the same.
5. Before combining, sometimes you need to the radicals by factoring out perfect squares.
6. Which of the following is equivalent to √50 + √32?
9√2
7√2
√82
9√4
7. What is the result of 6√20 - 2√45?
6√5
2√5
4√5
12√5
8. √(a+b) = √ a + √ b is a true statement for all positive real numbers a and b.
True
False
9. The expression 3√7 + 2√5 can be simplified further.
True
False
10. Simplify the expression: √(72x^3) + √(50x^3) - √(8x^3), assuming x ≥ 0.