How do you solve $$3c^2 - 17 = 10$$ ?

First, add 17 to both sides: $$3c^2 = 27$$ . Then divide by 3: $$c^2 = 9$$ . Finally, take the square root: $$c = \text{±3}$$ .

What is the solution set for $$k^2 - 6 = 43$$ ?

First, add 6 to both sides: $$k^2 = 49$$ . Then take the square root: $$k = 7, k = -7$$ .

How do you solve $$5(n - 7)^2 = 500$$ ?

First, divide by 5: $$(n - 7)^2 = 100$$ . Then take the square root: $$n - 7 = \text{±10}$$ . Thus, $$n = 17, n = -3$$ .

What is a radical expression?

A radical expression is an expression that includes a root, such as a square root, cube root, etc. For example, $$\text{√x}$$ is a radical expression.

How do you express a number in radical form?

To express a number in radical form, write it as a root. For example, the number 16 can be expressed as $$\text{√(16^2)}$$ .

What is the difference between rational and irrational numbers?

Rational numbers can be expressed as a fraction of two integers, while irrational numbers cannot be expressed as a simple fraction. For example, $$\text{√2}$$ is irrational.

What is the square of a binomial?

The square of a binomial is given by the formula: $$(a + b)^2 = a^2 + 2ab + b^2$$ .

How do you find the square root of a perfect square?

To find the square root of a perfect square, identify the number that, when multiplied by itself, gives the perfect square. For example, the square root of 25 is 5.

What is the relationship between exponents and square roots?

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

How do you check if a solution is correct for a square root equation?

To check if a solution is correct, substitute the solution back into the original equation and verify if both sides are equal.

Using Square Roots Flashcards

Student preview

14 questions

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1.

FLASHCARD QUESTION

Front

What is a square root?

Back

A square root of a number x is a value y such that y² = x. For example, the square root of 9 is 3, since 3² = 9.

2.

FLASHCARD QUESTION

Front

How do you simplify a square root?

Back

3.

FLASHCARD QUESTION

Front

What is the principal square root?

Back

The principal square root is the non-negative square root of a number. For example, the principal square root of 16 is 4.

4.

FLASHCARD QUESTION

Front

What does it mean to solve an equation involving square roots?

Back

To solve an equation involving square roots means to isolate the variable and find its value(s) that satisfy the equation.

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

Back

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