An nth root of a number 'a' is a number 'b' such that $$b^n = a$$ . It is denoted as $$\sqrt[n]{a}$$ .

What is the value of $$\sqrt[3]{-125}$$ ?

The value is -5, since $$(-5)^3 = -125$$ .

What is the value of $$\sqrt[6]{64}$$ ?

The value is 2, since $$2^6 = 64$$ .

What does the symbol $$\pm$$ represent in mathematics?

The symbol $$\pm$$ indicates that there are two possible values: one positive and one negative.

What is the value of $$\sqrt[2]{400}$$ ?

The value is $$\pm 20$$ , since both 20 and -20 squared give 400.

How do you simplify $$a^{\frac{1}{n}}$$ ?

$$a^{\frac{1}{n}}$$ simplifies to $$\sqrt[n]{a}$$ .

What is the value of $$\sqrt[4]{16}$$ ?

The value is 2, since $$2^4 = 16$$ .

What is the general formula for finding the nth root of a number?

The nth root of a number 'a' is given by $$\sqrt[n]{a}$$ .

What is the value of $$\sqrt[3]{27}$$ ?

The value is 3, since $$3^3 = 27$$ .

What is the value of $$\sqrt[2]{25}$$ ?

The value is $$\pm 5$$ , since both 5 and -5 squared give 25.

How do you express the cube root of a number using exponents?

The cube root of a number 'a' can be expressed as $$a^{\frac{1}{3}}$$ .

What is the value of $$\sqrt[5]{32}$$ ?

The value is 2, since $$2^5 = 32$$ .

What is the value of $$\sqrt[2]{81}$$ ?

The value is $$\pm 9$$ , since both 9 and -9 squared give 81.

What is the significance of the index in a root?

The index indicates the degree of the root; for example, a square root has an index of 2, and a cube root has an index of 3.

nth Roots and Rational Exponents

Flashcard

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Mathematics

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9th - 12th Grade

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Practice Problem

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Hard

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CCSS

8.EE.A.2, HSN.RN.A.2

Standards-aligned

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FLASHCARD QUESTION

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What is an nth root?

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FLASHCARD QUESTION

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CCSS.8.EE.A.2

FLASHCARD QUESTION

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What is the relationship between rational exponents and roots?

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CCSS.HSN.RN.A.2

FLASHCARD QUESTION

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Back

FLASHCARD QUESTION

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CCSS.8.EE.A.2

FLASHCARD QUESTION

Front

Back

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CCSS.8.EE.A.2

FLASHCARD QUESTION

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