How do you rationalize the denominator?

To rationalize the denominator, multiply the numerator and denominator by the conjugate of the denominator. For example, to rationalize $$\frac{1}{\text{√}2}$$ , multiply by $$\frac{\text{√}2}{\text{√}2}$$ .

What is the area of a rectangle with radical dimensions?

The area of a rectangle is calculated by multiplying its length and width. If the dimensions are $$18\text{√}20$$ and $$12\text{√}10$$ , then the area is $$18\text{√}20 \times 12\text{√}10 = 216\text{√}200$$ .

How do you simplify $$\text{√}45c^2$$ ?

To simplify $$\text{√}45c^2$$ , factor it as $$\text{√}(9 \times 5) \times \text{√}(c^2) = 3c\text{√}5$$ .

What is the process for simplifying $$\text{√}a^2b$$ ?

To simplify $$\text{√}a^2b$$ , take the square root of the perfect square: $$\text{√}a^2 = a$$ , so it simplifies to $$a\text{√}b$$ .

What is the value of $$\text{√}9 + \text{√}16$$ ?

$$\text{√}9 + \text{√}16 = 3 + 4 = 7$$ .

How do you multiply radical expressions?

To multiply radical expressions, multiply the numbers under the radicals and then simplify. For example, $$\text{√}2 \times \text{√}3 = \text{√}(2 \times 3) = \text{√}6$$ .

What is the square of a binomial involving radicals?

The square of a binomial is given by the formula: $$(a + b)^2 = a^2 + 2ab + b^2$$ . For example, $$(\text{√}2 + \text{√}3)^2 = 2 + 2\text{√}6 + 3 = 5 + 2\text{√}6$$ .

What is the significance of simplifying radicals in problem-solving?

Simplifying radicals makes calculations easier and helps in finding exact values, which is essential in algebra and geometry.

Operations with Radicals Flashcards

Student preview

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 inverse operation of exponentiation.

Tags

CCSS.8.NS.A.1

2.

FLASHCARD QUESTION

Front

How do you simplify a square root?

Back

3.

FLASHCARD QUESTION

Front

What is the product property of square roots?

Back

Tags

CCSS.HSN.RN.A.2

4.

FLASHCARD QUESTION

Front

What is the sum property of square roots?

Back

5.

FLASHCARD QUESTION

Front

How do you add or subtract radical expressions?

Back

6.

FLASHCARD QUESTION

Front

What is the difference between rational and irrational numbers?

Back

Tags

CCSS.8.NS.A.1

7.

FLASHCARD QUESTION

Front

What is the conjugate of a binomial?

Back

Tags

CCSS.HSN.CN.A.3

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