What is the square root of a variable squared, such as $$x^2$$ ?

The square root of $$x^2$$ is $$x$$ , assuming $$x$$ is non-negative.

How do you simplify $$\frac{\text{a}}{\text{b}}$$ when a and b are perfect squares?

You can simplify $$\frac{\text{a}}{\text{b}}$$ by taking the square root of both the numerator and the denominator separately.

What is the simplified form of $$\text{√}(a^2b)$$ ?

The simplified form is $$a\text{√}b$$ .

How do you simplify $$\text{√}(xy)$$ ?

You can express it as $$\text{√}x \text{√}y$$ .

What is the process to simplify $$\text{√}(75x^2)$$ ?

Factor 75 into 25 and 3, then take the square root of 25 (which is 5) and simplify to get $$5x\text{√}3$$ .

What is the simplified form of $$\text{√}(36x^3y^4)$$ ?

The simplified form is $$6y^2x\text{√}x$$ .

How do you simplify $$\text{√}(20a^2b^4)$$ ?

Factor 20 into 4 and 5, take the square root of 4 (which is 2), and simplify to get $$2ab^2\text{√}5$$ .

What is the rule for simplifying radicals with variables?

The rule is to separate the coefficients and variables, simplifying each part individually, and then combine the results.

What does it mean for a radical to be in simplest form?

A radical is in simplest form when there are no perfect square factors under the radical sign and no fractions under the radical.

How do you handle radicals with coefficients?

You can factor out the perfect squares from the coefficient and simplify them separately from the variable part.

What is the square root of $$x^4$$ ?

The square root of $$x^4$$ is $$x^2$$ .

What is the simplified form of $$\text{√}(x^2y^2)$$ ?

The simplified form is $$xy$$ .

Practice Simplify Radicals with Variables Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is a radical in mathematics?

Back

A radical is an expression that includes a root, such as a square root (√) or cube root (∛). It represents the inverse operation of exponentiation.

Tags

CCSS.8.NS.A.1

2.

FLASHCARD QUESTION

Front

What does it mean to simplify a radical?

Back

To simplify a radical means to express it in its simplest form, removing any perfect squares (or higher powers) from under the radical sign.

3.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.8.EE.A.2

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSN.RN.A.2

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

Back

The simplified form is 6, since 6 is the square root of 36.

Tags

CCSS.8.EE.A.2

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