Q#3 Radicals and Rational Exponentss

Front

What is a radical?

Back

A radical is an expression that includes a root, such as a square root (√) or cube root (∛). It represents the operation of finding a number that, when raised to a certain power, gives the original number.

Front

What is a rational exponent?

Back

Front

How do you simplify @@rac{ oot{a}}{ oot{b}}@@?

Back

You can simplify it to @@ oot{rac{a}{b}}@@.

Front

What is the relationship between radicals and rational exponents?

Back

Radicals can be expressed as rational exponents. For example, @@ oot[n]{x} = x^{rac{1}{n}}@@.

Front

How do you simplify @@ oot{a^2}@@?

Back

@@ oot{a^2} = a@@, assuming a is non-negative.

Front

What is the cube root of a number?

Back

Front

How do you combine like terms with radicals?

Back

You can combine like terms with radicals if they have the same index and radicand. For example, @@2 oot{5} + 3 oot{5} = 5 oot{5}@@.

Front

What is the process to rationalize the denominator?

Back

To rationalize the denominator, multiply the numerator and denominator by a suitable radical that will eliminate the radical in the denominator.

Front

Back

Front

What is the value of @@ oot[4]{x^{16}}@@?

Back

@@ oot[4]{x^{16}} = x^4@@.