Rationalize the denominator. 30/√5

Verified step by step guidance

1. Identify the expression to rationalize: \(\frac{30}{\sqrt{5}}\).
2. Recall that rationalizing the denominator means eliminating the square root from the denominator by multiplying numerator and denominator by the same radical.
3. Multiply both numerator and denominator by \(\sqrt{5}\) to get \(\frac{30}{\sqrt{5}} \times \frac{\sqrt{5}}{\sqrt{5}}\).
4. Use the property \(\sqrt{a} \times \sqrt{a} = a\) to simplify the denominator: \(\sqrt{5} \times \sqrt{5} = 5\).
5. Write the new expression as \(\frac{30 \times \sqrt{5}}{5}\) and simplify the fraction if possible.

Key Concepts

Rationalizing the Denominator

Rationalizing the denominator involves eliminating any irrational numbers, such as square roots, from the denominator of a fraction. This is done by multiplying both the numerator and denominator by a suitable expression that will remove the radical from the denominator.

Properties of Square Roots

Square roots have properties that allow simplification, such as √a × √a = a. Understanding these properties helps in manipulating expressions to rationalize denominators by converting radicals into whole numbers.

Multiplying Fractions by 1

Multiplying a fraction by a form of 1, such as √5/√5, changes the expression without altering its value. This technique is essential for rationalizing denominators because it allows the removal of radicals while keeping the fraction equivalent.