How do you simplify $$\text{√}12$$ ?

$$\text{√}12 = \text{√}(4 \times 3) = \text{√}4 \times \text{√}3 = 2\text{√}3$$ .

What is the square root of a negative number?

The square root of a negative number is expressed using the imaginary unit $$i$$ . For example, $$\text{√}(-4) = 2i$$ .

How do you simplify $$54\text{√}14 - 12\text{√}33$$ ?

This expression cannot be simplified further as the radicals are not like terms.

What is the difference between rational and irrational numbers?

Rational numbers can be expressed as a fraction of two integers, while irrational numbers cannot be expressed as a simple fraction. Examples: $$\frac{1}{2}$$ (rational) and $$\text{√}2$$ (irrational).

What is the principle of simplifying radicals?

The principle of simplifying radicals involves expressing the radical in its simplest form by factoring out perfect squares. For example, $$\text{√}18 = \text{√}(9 \times 2) = 3\text{√}2$$ .

How do you subtract radicals?

To subtract radicals, ensure they are like terms (same radicand). For example, $$5\text{√}2 - 3\text{√}2 = (5 - 3)\text{√}2 = 2\text{√}2$$ .

What is the square of a binomial?

The square of a binomial $$(a + b)$$ is given by the formula $$(a + b)^2 = a^2 + 2ab + b^2$$ .

How do you express a complex number in polar form?

A complex number $$a + bi$$ can be expressed in polar form as $$r(\text{cos} \theta + i \text{sin} \theta)$$ , where $$r = \text{√}(a^2 + b^2)$$ and $$\theta = \text{tan}^{-1}(\frac{b}{a})$$ .

What is the imaginary unit?

The imaginary unit, denoted as $$i$$ , is defined as $$i = \text{√}(-1)$$ , and it is used to express complex numbers.

Chapter 9 (Radicals and Complex Numbers) Review Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is a radical in mathematics?

Back

Tags

CCSS.8.NS.A.1

2.

FLASHCARD QUESTION

Front

Back

3.

FLASHCARD QUESTION

Front

What is the conjugate of a binomial expression?

Back

Tags

CCSS.HSN.CN.A.3

4.

FLASHCARD QUESTION

Front

How do you multiply radicals?

Back

5.

FLASHCARD QUESTION

Front

What is the process to rationalize the denominator?

Back

To rationalize the denominator, multiply the numerator and denominator by the conjugate of the denominator.

Tags

CCSS.HSN.RN.A.2

6.

FLASHCARD QUESTION

Front

What is a complex number?

Back

Tags

CCSS.HSN.CN.A.1

7.

FLASHCARD QUESTION

Front

How do you add complex numbers?

Back

Tags

CCSS.HSN.CN.A.2

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