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
Radicals with the same index and radicand.
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Adding/Subtracting Radicals
Adding/Subtracting Radicals
Combine like radicals by adding or subtracting their coefficients.
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Simplifying Before Adding/Subtracting
Simplifying Before Adding/Subtracting
Rewrite the radical, factoring out perfect square factors.
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Index of a Radical
Index of a Radical
The number indicating which root to take (square root, cube root, etc.)
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Coefficient of a Radical
Coefficient of a Radical
A number that multiplies a radical.
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Simplifying Square Roots
Simplifying Square Roots
Find the largest perfect square factor of the radicand.
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Simplifying √(xⁿ)
Simplifying √(xⁿ)
Divide the variable's exponent by 2. If odd, leave one 'x' inside.
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Radicals with Fractions
Radicals with Fractions
Simplify numerator and denominator separately, then eliminate radicals from the denominator.
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Rationalizing the Denominator
Rationalizing the Denominator
Removing radicals from the denominator of a fraction.
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Rationalizing with Conjugates
Rationalizing with Conjugates
Multiply the numerator and denominator by the conjugate of the denominator.
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Multiplying Radicals
Multiplying Radicals
Multiply the coefficients, then multiply the radicands. Simplify the result.
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Dividing Radicals
Dividing Radicals
Divide coefficients, divide radicands. Simplify, rationalize if needed.
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Squaring a Radical Expression
Squaring a Radical Expression
Multiply the radical expression by itself.
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Conjugates
Conjugates
Binomials that differ only in the sign separating the terms.
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Multiplying coefficients and radicals.
Multiplying coefficients and radicals.
Multiply, the outer numbers need to be multiplied and the radicals need to be multiplied
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Finding common factors
Finding common factors
Find common factors to simplify complex radical equations.
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Rationalize
Rationalize
Ensure that there are no radicals in the denominator.
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Simplifying first
Simplifying first
Always look for a way to simplifying the equation to make it small.
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- 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.
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