Can we write √20 as 2 √ 5?

Simplifying Radicals: Can We Write $\sqrt{20}$ as $2\sqrt{5}$?

When working with square roots in algebra, numbers are not always left in their initial form. A common question is whether the square root of twenty can be expressed differently, specifically as $2\sqrt{5}$.

The short answer is yes. In mathematics, expressions under a radical sign—known as radicands—can often be simplified by factoring out perfect squares. To break down $\sqrt{20}$, you look for the largest square number that divides evenly into twenty. That number is four.

By splitting the expression into the product of two separate roots, you get $\sqrt{4 \times 5}$, which can be rewritten as $\sqrt{4} \times \sqrt{5}$. Because the square root of four simplifies neatly to two, the entire expression becomes $2\sqrt{5}$.

This technique is essential for solving equations, combining like terms, and keeping fractions in their cleanest, most reduced form.