Add and Subtract Radicals

Flashcard
•
Mathematics
•
9th - 12th Grade
•
Hard
Standards-aligned
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15 questions
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1.
FLASHCARD QUESTION
Front
What is a radical in mathematics?
Back
A radical is an expression that includes a root, such as a square root (√) or cube root (∛). It represents the operation of finding a number that, when multiplied by itself a certain number of times, gives the original number.
Tags
CCSS.8.NS.A.1
2.
FLASHCARD QUESTION
Front
How do you simplify a radical expression?
Back
To simplify a radical expression, factor the number under the radical into its prime factors, and then take out pairs of factors for square roots (or appropriate groups for higher roots). For example, √18 = √(9*2) = 3√2.
3.
FLASHCARD QUESTION
Front
What does it mean to add radicals?
Back
To add radicals, you can only combine them if they have the same index and radicand. For example, √2 + √2 = 2√2, but √2 + √3 cannot be simplified further.
4.
FLASHCARD QUESTION
Front
What is the process for subtracting radicals?
Back
Subtracting radicals follows the same rules as adding them. You can only subtract radicals with the same index and radicand. For example, 3√5 - 2√5 = (3-2)√5 = 1√5.
5.
FLASHCARD QUESTION
Front
What is the index of a radical?
Back
The index of a radical indicates the degree of the root being taken. For example, in the square root √x, the index is 2 (implied), and in the cube root ∛x, the index is 3.
6.
FLASHCARD QUESTION
Front
Can you add or subtract different radicals?
Back
No, you cannot add or subtract different radicals (e.g., √2 + √3) because they do not have the same radicand. They remain separate terms.
7.
FLASHCARD QUESTION
Front
What is a perfect square?
Back
A perfect square is a number that can be expressed as the square of an integer. For example, 1, 4, 9, 16, and 25 are perfect squares.
Tags
CCSS.6.EE.A.1
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