# How do you simplify sqrt10*sqrt20?

Jan 24, 2017

$10 \sqrt{2}$

#### Explanation:

Using the property that states that $\sqrt{a} \sqrt{b} = \sqrt{a b}$,

$\sqrt{10} \cdot \sqrt{20} = \sqrt{10 \cdot 20} = \sqrt{200} = \sqrt{25 \cdot 4 \cdot 2}$

$= \sqrt{25} \sqrt{4} \sqrt{2} = 5 \cdot 2 \cdot \sqrt{2} = 10 \sqrt{2}$.

Jan 24, 2017

Multiply the two radicals together, then simplify the result. Details below...
The result is $10 \sqrt{2}$

#### Explanation:

First, since square root is the same as using the exponent $\frac{1}{2}$ the two radicals obey the rule

${a}^{x} \cdot {b}^{x} = {\left(a \cdot b\right)}^{x}$

So ${10}^{\frac{1}{2}} \cdot {20}^{\frac{1}{2}} = {200}^{\frac{1}{2}}$ or $\sqrt{200}$

Next, look for the largest factor of 200 that is a perfect square. This is $100 \times 2$

So, $\sqrt{200} = \sqrt{100} \cdot \sqrt{2} = 10 \sqrt{2}$