Question

Simplify the radical expression. $$4 \sqrt{\frac{5}{4}}$$

Short answer

The simplified form of the radical expression is \(2\sqrt{5}\).

Step-by-step solution

Simplify the Fraction inside the Root

The fraction inside the root is already simplified, so there's no need to simplify further. In other words, it's already in its simplified form: \( \frac{5}{4} \)

Square Root the Simplified Fraction

Take the square root of the simplified fraction. The square root of a fraction is the square root of the numerator divided by the square root of the denominator. Therefore, \(\sqrt{\frac{5}{4}}\) simplifies to \(\frac{\sqrt{5}}{\sqrt{4}}\), which further simplifies to \(\frac{\sqrt{5}}{2}\).

Multiply Constant with Simplified Root

Multiply the simplified root by the constant outside the root. This gives: \(4 \times \frac{\sqrt{5}}{2}\). This simplifies to \(2\sqrt{5}\).