How would you simplify sqrt2 times 5 sqrt2?

Apr 21, 2018

$10$

Explanation:

Multiplying radicals is similar to regular multiplying. You will multiply the terms outside the square roots together and multiply the terms inside the square root together.

$\sqrt{2} \times 5 \sqrt{2}$

Let's change it a little to give the first quantity a number outside the square root:

$1 \sqrt{2} \times 5 \sqrt{2}$

Anything multiplied by $1$ is itself, so it doesn't change the value of the expression for it to be there.

Now multiply the outside numbers and inside numbers together:

$1 \times 5 \sqrt{2 \times 2}$

$5 \sqrt{4}$

$5 \left(2\right) \rightarrow 10$

Apr 22, 2018

$10$

Explanation:

Given: $\sqrt{2} \cdot 5 \sqrt{2}$

Rearrange into:

$\implies \sqrt{2} \cdot \sqrt{2} \cdot 5$

$= {\left(\sqrt{2}\right)}^{2} \cdot 5$

$= 2 \cdot 5$

$= 10$