How do you rationalize the denominator of $$\frac{2 - \sqrt{5}}{6 + 2\sqrt{5}}$$ ?

The simplified form after rationalizing is $$\frac{11-5 \sqrt[]{5}}{8}$$ .

Simplify $$\frac{y^2}{y^7}$$ using only positive exponents.

The simplified form is $$\frac{1}{y^5}$$ .

Factor the expression $$6w + 12$$ .

The factored form is $$6(w+2)$$ .

What is the simplified form of $$\frac{-8}{2 \sqrt[]{3}-2}$$ after rationalizing the denominator?

The simplified form is $$-2-2 \sqrt[]{3}$$ .

What is the rule for simplifying exponents when dividing?

When dividing like bases, subtract the exponents: $$\frac{a^m}{a^n} = a^{m-n}$$ .

What is the process for factoring a common factor from an expression?

To factor out a common factor, divide each term by the common factor and write it outside the parentheses.

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.

What is the formula for rationalizing a binomial denominator?

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

What is the significance of positive exponents in algebra?

Positive exponents indicate the number of times a base is multiplied by itself, while negative exponents represent the reciprocal of the base raised to the positive exponent.

What is the result of factoring $$x^2 - 9$$ ?

The factored form is $$(x-3)(x+3)$$ .

What is the formula for the difference of squares?

The difference of squares can be factored using the formula: $$a^2 - b^2 = (a-b)(a+b)$$ .

What is the process for simplifying a complex fraction?

To simplify a complex fraction, multiply the numerator and denominator by the least common denominator (LCD) of the fractions involved.

Pre-Cal Fall Semester Final Exam (2024) Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA.APR.D.6

2.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSN.RN.A.2

3.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.8.EE.A.1

4.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.7.EE.A.1

5.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSN.RN.A.2

6.

FLASHCARD QUESTION

Front

Define rationalizing the denominator.

Back

Rationalizing the denominator is the process of eliminating any square roots or irrational numbers from the denominator of a fraction.

Tags

CCSS.HSN.RN.A.2

7.

FLASHCARD QUESTION

Front

What is the formula for multiplying fractions?

Back

Tags

CCSS.5.NF.B.6

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