Algebra: Roots and Radicals flashcards

Question 1

If n^2 = m, what is m called?

Accepted Answer

The square of n.

Question 2

If n^2 = m, what is n called?

Accepted Answer

A square root of m.

Question 3

How many square roots does a positive number have?

Accepted Answer

Two: one positive and one negative.

Question 4

What is the principal square root of a positive number?

Accepted Answer

Its positive square root.

Question 5

Is the square root of a negative number a real number?

Accepted Answer

No.

Question 6

If b^n = a, what is b?

Accepted Answer

An nth root of a.

Question 7

In the radical ⁿ√a, what is n called?

Accepted Answer

The index of the radical.

Question 8

State the Product Property of Square Roots.

Accepted Answer

For non-negative real a and b, √(ab) = √a · √b.

Question 9

State the Quotient Property of Square Roots.

Accepted Answer

For non-negative real a and b with b ≠ 0, √(a/b) = √a / √b.

Question 10

When is √a considered simplified (regarding factors of a)?

Accepted Answer

When a has no perfect-square factors.

Question 11

Can a simplified square root have a square root in the denominator of a fraction?

Accepted Answer

No.

Question 12

Why must you check answers after squaring both sides of a radical equation?

Accepted Answer

Some solutions found may not satisfy the original equation.

Question 13

For an even index n and a < 0, is ⁿ√a a real number?

Accepted Answer

No.

Question 14

For an odd index n, for which values of a is ⁿ√a a real number?

Accepted Answer

All values of a.

Question 15

For an integer n ≥ 2 that is odd, what is ⁿ√(a^n)?

Accepted Answer

a

Question 16

For an integer n ≥ 2 that is even, what is ⁿ√(a^n)?

Accepted Answer

|a|

Question 17

If ⁿ√a is a real number and n ≥ 2, what is a^(1/n)?

Accepted Answer

ⁿ√a

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