Adding and Subtracting Radicals

Front

What is a radical in mathematics?

Back

A radical is an expression that includes a root, such as a square root or cube root. The most common radical is the square root, denoted by the symbol \( \sqrt{} \).

Front

How do you simplify \( \sqrt{24} \)?

Back

To simplify \( \sqrt{24} \), factor it into \( \sqrt{4 \cdot 6} = \sqrt{4} \cdot \sqrt{6} = 2\sqrt{6} \).

Front

What is the first step in adding or subtracting radicals?

Back

The first step is to simplify the radicals, if possible, to see if they can be combined.

Front

Can you add \( 3\sqrt{2} \) and \( 5\sqrt{2} \)? If so, what is the result?

Back

Yes, you can add them. \( 3\sqrt{2} + 5\sqrt{2} = (3 + 5)\sqrt{2} = 8\sqrt{2} \).

Front

What is the result of \( -3\sqrt{6} + 5\sqrt{24} \)?

Back

First, simplify \( 5\sqrt{24} \) to \( 10\sqrt{6} \). Then, combine: \( -3\sqrt{6} + 10\sqrt{6} = 7\sqrt{6} \).

Front

What does it mean for radicals to be 'like terms'?

Back

Radicals are 'like terms' if they have the same index and radicand. For example, \( 2\sqrt{3} \) and \( 5\sqrt{3} \) are like terms.

Front

How do you subtract \( 4\sqrt{5} \) from \( 6\sqrt{5} \)?

Back

You subtract them as follows: \( 6\sqrt{5} - 4\sqrt{5} = (6 - 4)\sqrt{5} = 2\sqrt{5} \).

Front

What is the result of \( \sqrt{a} + \sqrt{a} \)?

Back

The result is \( 2\sqrt{a} \).

Front

How do you handle radicals with different radicands when adding or subtracting?

Back

You cannot combine radicals with different radicands. For example, \( \sqrt{2} + \sqrt{3} \) cannot be simplified further.

Front

What is the simplified form of \( \sqrt{50} \)?

Back

The simplified form of \( \sqrt{50} \) is \( 5\sqrt{2} \) because \( \sqrt{50} = \sqrt{25 \cdot 2} = 5\sqrt{2} \).