How do you simplify $$18\\sqrt{20}$$ ?

First, simplify $$\\sqrt{20} = \\sqrt{4 \times 5} = 2\\sqrt{5}$$ . Then, $$18\\sqrt{20} = 18 \times 2\\sqrt{5} = 36\\sqrt{5}$$ .

What is the formula for the area of a rectangle with radical dimensions?

If a rectangle has dimensions of $$a\\sqrt{b}$$ and $$c\\sqrt{d}$$ , then the area is $$\text{Area} = (a\\sqrt{b}) \times (c\\sqrt{d}) = ac\\sqrt{bd}$$ .

How do you multiply radicals?

To multiply radicals, multiply the numbers outside the radicals and the numbers inside the radicals separately. For example, $$\\sqrt{a} \times \\sqrt{b} = \\sqrt{a \times b}$$ .

What is the square of a radical?

The square of a radical is found by squaring the number inside the radical. For example, $$(\\sqrt{a})^2 = a$$ .

How do you rationalize the denominator?

To rationalize the denominator, multiply the numerator and denominator by a radical that will eliminate the radical in the denominator. For example, to rationalize $$\frac{1}{\sqrt{2}}$$ , multiply by $$\frac{\sqrt{2}}{\sqrt{2}}$$ .

What is the difference between a perfect square and a non-perfect square?

A perfect square is a number that can be expressed as the square of an integer (e.g., 1, 4, 9), while a non-perfect square cannot (e.g., 2, 3, 5).

How do you find the area of a rectangle with radical dimensions?

If the dimensions are given as radicals, multiply the coefficients and the radicals separately. For example, if the dimensions are $$3\\sqrt{2}$$ and $$4\\sqrt{3}$$ , then the area is $$12\\sqrt{6}$$ .

Mixed Operations with Radicals Flashcards

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FLASHCARD QUESTION

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 (∛). It represents the inverse operation of exponentiation.

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