Multiplying Radicals

Front

What is a radical in mathematics?

Back

A radical is a symbol that represents the root of a number, most commonly the square root. For example, √4 represents the square root of 4.

Front

What is the product of two square roots?

Back

The product of two square roots can be simplified using the property: √a · √b = √(a · b).

Front

How do you simplify the expression √a + √b?

Back

The expression √a + √b cannot be simplified further unless a and b are perfect squares or have common factors.

Front

What is the result of multiplying a radical by a whole number?

Back

When multiplying a radical by a whole number, you can place the whole number outside the radical. For example, 3√2 remains as is.

Front

How do you simplify √(a^2)?

Back

The simplification of √(a^2) is |a|, which means the absolute value of a.

Front

What is the distributive property in relation to radicals?

Back

The distributive property states that a(b + c) = ab + ac. This applies to radicals as well, such as a√b(c + d) = a√b·c + a√b·d.

Front

What is the result of √(x^2) when x is negative?

Back

When x is negative, √(x^2) = -x, since the square root function returns the principal (non-negative) root.

Front

How do you multiply two radicals with different radicands?

Back

To multiply two radicals with different radicands, you can multiply the numbers inside the radicals: √a · √b = √(a · b).

Front

What is the simplified form of √(a^2b)?

Back

The simplified form of √(a^2b) is a√b, assuming a is non-negative.

Front

How do you simplify the expression √(12)?

Back

To simplify √(12), factor it into √(4 · 3) = √4 · √3 = 2√3.