Multiply Square Roots: Solving √5 × √5

Think of it this way: $\sqrt{5}$ means "what number times itself equals 5?" So $\sqrt{5} \times \sqrt{5}$ is asking "what number times itself, times itself again?" That's just 5!

Yes! Any square root multiplied by itself always equals the number under the radical. So $\sqrt{n} \cdot \sqrt{n} = n$ for any positive number n.

When the radicands are different, you multiply them: $\sqrt{3} \times \sqrt{7} = \sqrt{21}$. But when they're identical, like $\sqrt{5} \times \sqrt{5}$, you get just the radicand: 5.

Converting to exponents helps! $\sqrt{5} = 5^{\frac{1}{2}}$, so $\sqrt{5} \times \sqrt{5} = 5^{\frac{1}{2}} \times 5^{\frac{1}{2}} = 5^{\frac{1}{2} + \frac{1}{2}} = 5^1 = 5$

Absolutely! Since $\sqrt{5} \approx 2.236$, multiply: $2.236 \times 2.236 \approx 5$. This confirms our exact answer of 5!