Review Unit 4: Nth Roots

Front

What is an nth root?

Back

An nth root of a number x is a number r such that r^n = x. It is denoted as \( \sqrt[n]{x} \).

Front

How do you simplify \( \sqrt{a^2} \)?

Back

\( \sqrt{a^2} = |a| \) because the square root of a square is the absolute value of the original number.

Front

What is the relationship between rational exponents and roots?

Back

Rational exponents can be expressed as roots. For example, \( a^{m/n} = \sqrt[n]{a^m} \).

Front

How do you solve the equation \( \sqrt{x+1} = x-1 \)?

Back

Square both sides to eliminate the square root: \( x + 1 = (x - 1)^2 \). This leads to the solutions x = 3 and x = -1.

Front

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

Back

The value of \( \sqrt[3]{27} \) is 3, since 3^3 = 27.

Front

How do you rewrite \( \sqrt{x} \) using rational exponents?

Back

\( \sqrt{x} \) can be rewritten as \( x^{1/2} \).

Front

What is the solution to the equation \( x^2 = 64 \)?

Back

The solutions are x = 8 and x = -8, since both satisfy the equation.

Front

What does it mean if an equation has 'no solution'?

Back

An equation has 'no solution' if there are no values of the variable that satisfy the equation.

Front

How do you express \( (2x+1)^{3/4} \) using a radical?

Back

\( (2x+1)^{3/4} = \sqrt[4]{(2x+1)^3} \).

Front

What is the principal square root of 16?

Back

The principal square root of 16 is 4, as it is the non-negative root.