What is the conjugate of $$5 + \sqrt{7}$$ ?

The conjugate is $$5 - \sqrt{7}$$ .

Simplify $$\sqrt{200}$$ .

The simplified form is $$10\sqrt{2}$$ .

Rationalize the denominator of $$\frac{7\sqrt{3}}{4\sqrt{7}}$$ .

The rationalized form is $$\frac{\sqrt{21}}{4}$$ .

Simplify the radical $$\sqrt{150}$$ .

The simplified form is $$5\sqrt{6}$$ .

What does it mean to rationalize the denominator?

Rationalizing the denominator means to eliminate any square roots or irrational numbers from the denominator.

What is the quadratic formula?

The quadratic formula is $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ .

What is the difference between rational and irrational numbers?

Rational numbers can be expressed as a fraction of two integers, while irrational numbers cannot.

What is the process to solve a quadratic equation?

Set the equation to zero, factor if possible, or use the quadratic formula.

What is a radical expression?

A radical expression contains a root, such as a square root, cube root, etc.

How do you combine like terms in algebra?

Add or subtract the coefficients of terms that have the same variable raised to the same power.

What is the Pythagorean theorem?

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides: $$a^2 + b^2 = c^2$$ .

What is the importance of the discriminant in a quadratic equation?

The discriminant determines the nature of the roots: if positive, two real roots; if zero, one real root; if negative, no real roots.

6.1 Practice Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

Back

2.

FLASHCARD QUESTION

Front

Back

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

Solve the equation: 5b^2 - 4 = 41.

Back

The solution is b = ±3.

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

What is a conjugate in mathematics?

Back

The conjugate of a binomial expression is formed by changing the sign between the two terms.

7.

FLASHCARD QUESTION

Front

How do you simplify a square root?

Back

Factor the number under the square root into its prime factors and simplify by taking out pairs.

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