Rationalize the denominator. 30/√5

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Identify the expression to rationalize: $\frac{30}{\sqrt{5}}$.

Recall that rationalizing the denominator means eliminating the square root from the denominator by multiplying numerator and denominator by the same radical.

Multiply both numerator and denominator by $\sqrt{5}$ to get $\frac{30}{\sqrt{5}} \times \frac{\sqrt{5}}{\sqrt{5}}$.

Use the property $\sqrt{a} \times \sqrt{a} = a$ to simplify the denominator: $\sqrt{5} \times \sqrt{5} = 5$.

Write the new expression as $\frac{30 \times \sqrt{5}}{5}$ and simplify the fraction if possible.

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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.

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Rationalizing Denominators

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.

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Imaginary Roots with the Square Root Property

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.

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