What does it mean to simplify a square root?

To simplify a square root means to express it in its simplest form, removing any perfect squares from under the radical.

What is a perfect square?

A perfect square is an integer that is the square of another integer, e.g., 1, 4, 9, 16, etc.

What is the result of $$\sqrt{a^2}$$ ?

$$\sqrt{a^2} = |a|$$ , which is the absolute value of a.

What is the relationship between square roots and exponents?

The square root of a number can be expressed as an exponent: $$\sqrt{a} = a^{1/2}$$ .

How do you solve $$x^2 = 25$$ ?

Using the square root property, $$x = \text{±}5$$ .

What is the formula for the difference of squares?

The difference of squares formula states that $$a^2 - b^2 = (a - b)(a + b)$$ .

What is the importance of the square root property in solving equations?

The square root property allows us to find solutions to quadratic equations by taking the square root of both sides.

Dividing Square Roots And Square Root Property

Dividing Square Roots and Square Root Property

Flashcard

•

Mathematics

•

9th - 12th Grade

•

Practice Problem

•

Hard

•

CCSS

HSA-REI.B.4B, 8.EE.A.2, HSN.RN.A.2

Standards-aligned

Wayground Content

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Student preview

15 questions

Show all answers

FLASHCARD QUESTION

Front

What is the square root property?

Back

The square root property states that if $x^2 = a$ , then $x = \text{±}\sqrt{a}$ . This is used to solve quadratic equations.

Tags

CCSS.HSA-REI.B.4B

FLASHCARD QUESTION

Front

Simplify $\frac{8\sqrt{20}}{4\sqrt{5}}$

Back

$4$

Tags

CCSS.HSN.RN.A.2

FLASHCARD QUESTION

Front

Solve for x: $x^2 - 5 = 31$

Back

$x = \text{±}6$

Tags

CCSS.8.EE.A.2

FLASHCARD QUESTION

Front

Solve using square roots: $k^2 - 6 = 43$

Back

$k = 7, k = -7$

Tags

CCSS.8.EE.A.2

FLASHCARD QUESTION

Front

Solve by taking square roots: $k^2 - 6 = -50$

Back

$k = \text{±}2i\sqrt{11}$

Tags

CCSS.HSA-REI.B.4B

FLASHCARD QUESTION

Front

Simplify $\frac{6\sqrt{18}}{2\sqrt{3}}$

Back

$3\sqrt{6}$

Tags

CCSS.HSN.RN.A.2

FLASHCARD QUESTION

Front

What is the definition of a square root?

Back

A square root of a number $a$ is a number $b$ such that $b^2 = a$ .

Tags

CCSS.8.EE.A.2

10.

FLASHCARD QUESTION

Front

How do you simplify $\sqrt{a} \cdot \sqrt{b}$ ?

Back

$\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}$ .

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