1-7 Day #1: Multiplying Radicals/ Review (1-20)

Front

What is the product of two square roots, \(\sqrt{a} \cdot \sqrt{b}\)?

Back

The product is \(\sqrt{a \cdot b}\).

Front

How do you simplify \(\sqrt{30} \cdot \sqrt{20}\)?

Back

You can simplify it to \(10\sqrt{6}\).

Front

What is the result of \(3\sqrt{6} \left(\sqrt{6} - 2\sqrt{10}\right)\)?

Back

The result is \(18 - 12\sqrt{15}\).

Front

How do you express \(4^{4/3}\) in radical form?

Back

It can be expressed as \(\sqrt[3]{4^4} = \sqrt[3]{256}\).

Front

What is the simplified form of \(3^3 \sqrt{2}\)?

Back

It is \(27\sqrt{2}\).

Front

What is the definition of a radical?

Back

A radical is an expression that includes a root, such as a square root or cube root.

Front

What is the square root of a product?

Back

The square root of a product is equal to the product of the square roots: \(\sqrt{ab} = \sqrt{a} \cdot \sqrt{b}\).

Front

How do you simplify \(\sqrt{a^2} \)?

Back

It simplifies to \(|a|\).

Front

What is the principle of simplifying radicals?

Back

The principle involves breaking down the radicand into its prime factors and simplifying where possible.

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.