Operations with Radicals

Front

What is a radical in mathematics?

Back

A radical is a symbol used to represent the root of a number, most commonly the square root.

Front

How do you simplify √a + √b?

Back

You can simplify √a + √b only if a and b are perfect squares or if they can be expressed as a common radical.

Front

What is the process for simplifying √(a*b)?

Back

The process involves taking the square root of each factor separately: √(a*b) = √a * √b.

Front

How do you simplify expressions involving coefficients and radicals, such as 3√2 + 2√2?

Back

You can combine like terms: 3√2 + 2√2 = (3 + 2)√2 = 5√2.

Front

What is the value of √(x^2)?

Back

The value of √(x^2) is |x|, the absolute value of x.

Front

How do you simplify √(a^2 * b)?

Back

You can simplify it to a√b, assuming a is non-negative.

Front

What is the difference between rational and irrational numbers?

Back

Rational numbers can be expressed as a fraction of two integers, while irrational numbers cannot be expressed as such.

Front

What is the principle of combining radicals?

Back

You can combine radicals when they have the same index and radicand.

Front

How do you rationalize the denominator of a fraction like 1/√2?

Back

Multiply the numerator and denominator by √2 to get √2/2.

Front

What is the result of √(x^2 + 2x + 1)?

Back

The result is √((x+1)^2) = |x+1|.