Question

How do you simplify `sqrt3sqrt21`?

Answer 1

I get `3\sqrt{7}`, see below.

Explanation:

Factor the 21 and write each factor as its own square toot:

`21=3×7` so `\sqrt{21}=\sqrt{3}×\sqrt{7}`

You Can't do this with the `\sqrt{3}` factor because 3 is,already prime. But you can find a pair of like square roots now in the product `\sqrt{3}\sqrt{21}`:

`\sqrt{3}\sqrt{21}=\sqrt{3}×(\sqrt{3}×\sqrt{7})`

`=(\sqrt{3}×\sqrt{3})×\sqrt{7}`

`=(\sqrt{3})^2×\sqrt{7}`

`=color(blue)(3\sqrt{7})`

Answer 2

`3sqrt7`

Explanation:

`"using the "color(blue)"law of radicals"`

`•color(white)(x)sqrtaxxsqrtbhArrsqrt(ab)`

`rArrsqrt3xxsqrt21=sqrt(3xx21)=sqrt63`

`sqrt63=sqrt(9xx7)=sqrt9xxsqrt7=3sqrt7`