5.1 Simplify Radicals version2

Front

What does it mean to simplify a radical expression?

Back

To simplify a radical expression means to express it in its simplest form, removing any perfect square factors from under the radical sign.

Front

What is the simplified form of \( \sqrt{242} \)?

Back

The simplified form of \( \sqrt{242} \) is \( 11\sqrt{2} \).

Front

Identify a perfect square from the list: 1, 4, 9, 27, 81, 100, 200.

Back

The perfect squares from the list are 1, 4, 9, 81, and 100. 27 and 200 are not perfect squares.

Front

What is the simplified form of \( \sqrt{300} \)?

Back

The simplified form of \( \sqrt{300} \) is \( 10\sqrt{3} \).

Front

What is the simplified form of \( \sqrt{40} \)?

Back

The simplified form of \( \sqrt{40} \) is \( 2\sqrt{10} \).

Front

What is a perfect square?

Back

A perfect square is a number that can be expressed as the square of an integer.

Front

How do you determine if a number is a perfect square?

Back

To determine if a number is a perfect square, find its square root and check if the result is an integer.

Front

What is the product property of square roots?

Back

The product property states that \( \sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b} \) for any non-negative numbers a and b.

Front

What is the quotient property of square roots?

Back

The quotient property states that \( \frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}} \) for any non-negative numbers a and b, where b is not zero.

Front

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

Back

The simplified form of \( \sqrt{a^2} \) is |a|, the absolute value of a.