Simplifying Perfect nth roots

Front

What is a perfect nth root?

Back

A perfect nth root of a number is a value that, when raised to the power of n, gives the original number. For example, the perfect square root of 9 is 3, because 3^2 = 9.

Front

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

Back

To simplify the square root of a perfect square, take the square root of the number. For example, √16 = 4.

Front

What is the cube root of 27?

Back

The cube root of 27 is 3, because 3^3 = 27.

Front

How do you express the nth root of a number in exponential form?

Back

The nth root of a number 'a' can be expressed as a^(1/n). For example, the square root of a is a^(1/2).

Front

What is the relationship between exponents and roots?

Back

Exponents and roots are inversely related; raising a number to a power and taking a root are opposite operations. For example, (a^(1/n))^n = a.

Front

How do you simplify the expression √(a^2)?

Back

The expression √(a^2) simplifies to |a|, which is the absolute value of a.

Front

What is the fourth root of 16?

Back

The fourth root of 16 is 2, because 2^4 = 16.

Front

How do you simplify the cube root of a product?

Back

The cube root of a product can be simplified using the property: ∛(a*b) = ∛a * ∛b.

Front

What is the perfect square of 12?

Back

The perfect square of 12 is 144, because 12^2 = 144.

Front

How do you simplify the expression ∛(x^3)?

Back

The expression ∛(x^3) simplifies to x.