Podcast
Questions and Answers
Simplify the expression $\sqrt{275}$. Which of the following is the correct simplified radical form?
Simplify the expression $\sqrt{275}$. Which of the following is the correct simplified radical form?
- $25\sqrt{11}$
- $5\sqrt{11}$ (correct)
- $5\sqrt{55}$
- $11\sqrt{5}$
Simplify the expression $-4\sqrt{108}$. Which of the following represents its simplest radical form?
Simplify the expression $-4\sqrt{108}$. Which of the following represents its simplest radical form?
- $-12\sqrt{3}$
- $-4\sqrt{3}$
- $-12\sqrt{6}$
- $-24\sqrt{3}$ (correct)
Simplify the cube root: $\sqrt[3]{135}$. Which of the following is the correct simplification?
Simplify the cube root: $\sqrt[3]{135}$. Which of the following is the correct simplification?
- $5\sqrt[3]{3}$
- $\sqrt[3]{135}$ (correct)
- $3\sqrt[3]{5}$
- $3\sqrt[3]{15}$
Simplify the radical expression $4\sqrt[3]{-88}$. Which of the following represents the simplified form?
Simplify the radical expression $4\sqrt[3]{-88}$. Which of the following represents the simplified form?
Simplify the expression $-2\sqrt{196k^8}$. What is the simplified form, assuming k is non-negative?
Simplify the expression $-2\sqrt{196k^8}$. What is the simplified form, assuming k is non-negative?
Simplify the expression $5\sqrt{147x^9y^{16}z^2}$. Assuming x, y, and z are non-negative, which of the following is the simplified form?
Simplify the expression $5\sqrt{147x^9y^{16}z^2}$. Assuming x, y, and z are non-negative, which of the following is the simplified form?
Simplify the expression $-5\sqrt{2} - 3\sqrt{2}$. What is the result?
Simplify the expression $-5\sqrt{2} - 3\sqrt{2}$. What is the result?
Which of the following statements accurately describes the process of simplifying a radical?
Which of the following statements accurately describes the process of simplifying a radical?
When simplifying a square root containing a variable with an odd exponent, such as $\sqrt{x^7}$, what is the correct procedure?
When simplifying a square root containing a variable with an odd exponent, such as $\sqrt{x^7}$, what is the correct procedure?
What is the primary goal when rationalizing the denominator of a fraction containing a radical?
What is the primary goal when rationalizing the denominator of a fraction containing a radical?
What is the result of squaring the radical expression $(4\sqrt{5})^2$?
What is the result of squaring the radical expression $(4\sqrt{5})^2$?
Simplify the expression $\sqrt{75x^3y^2}$, assuming x and y are non-negative.
Simplify the expression $\sqrt{75x^3y^2}$, assuming x and y are non-negative.
Rationalize the denominator: $\frac{3}{\sqrt{5}}$
Rationalize the denominator: $\frac{3}{\sqrt{5}}$
Simplify: $2\sqrt{45} - \sqrt{20}$
Simplify: $2\sqrt{45} - \sqrt{20}$
Flashcards
Simplifying Radicals
Simplifying Radicals
Breaking down a radical into its factors to find perfect squares (or cubes, etc.)
Perfect Square
Perfect Square
A number that can be expressed as the product of an integer by itself.
Radicand
Radicand
A number that is to be rooted
Like Radicals
Like Radicals
Signup and view all the flashcards
Adding/Subtracting Radicals
Adding/Subtracting Radicals
Signup and view all the flashcards
Simplifying Before Adding/Subtracting
Simplifying Before Adding/Subtracting
Signup and view all the flashcards
Index of a Radical
Index of a Radical
Signup and view all the flashcards
Coefficient of a Radical
Coefficient of a Radical
Signup and view all the flashcards
Simplifying Square Roots
Simplifying Square Roots
Signup and view all the flashcards
Simplifying √(xⁿ)
Simplifying √(xⁿ)
Signup and view all the flashcards
Radicals with Fractions
Radicals with Fractions
Signup and view all the flashcards
Rationalizing the Denominator
Rationalizing the Denominator
Signup and view all the flashcards
Rationalizing with Conjugates
Rationalizing with Conjugates
Signup and view all the flashcards
Multiplying Radicals
Multiplying Radicals
Signup and view all the flashcards
Dividing Radicals
Dividing Radicals
Signup and view all the flashcards
Squaring a Radical Expression
Squaring a Radical Expression
Signup and view all the flashcards
Conjugates
Conjugates
Signup and view all the flashcards
Multiplying coefficients and radicals.
Multiplying coefficients and radicals.
Signup and view all the flashcards
Finding common factors
Finding common factors
Signup and view all the flashcards
Rationalize
Rationalize
Signup and view all the flashcards
Simplifying first
Simplifying first
Signup and view all the flashcards
Study Notes
- Quiz 10-1 covers simplifying, adding, and subtracting radicals.
Problems
- √275 needs to be simplified to its simplest radical form.
- -4√108 needs to be simplified to its simplest radical form.
- The cube root of 135 (∛135) needs to be simplified.
- 4 times the cube root of -88 (4∛-88) needs to be simplified.
- -2√(196k⁸) needs to be simplified.
- 5√(147x⁹y¹⁶z²) needs to be simplified.
- -5√2 - 3√2 needs to be simplified.
- 2√7 + 3√28 needs to be simplified.
- 8√75 - √192 + 4√6 needs to be simplified.
- 4√125 - 2√243 - 3√20 + 5√27 needs to be simplified.
Bonus
- 5x²√(18xy) + √(72x⁵y) - x²√(2xy) needs to be simplified.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Related Documents
Description
Simplify radicals to simplest form. Add and subtract expressions containing radicals. Problems include square roots and cube roots with both numeric and algebraic terms.
