QuestionConvert to an entire radical: a. $2 \sqrt{3}$

Studdy Solution

STEP 1

1. We are given the expression $2 \sqrt{3}$ and need to convert it to an entire radical.
2. An entire radical is a radical expression where the coefficient is incorporated under the radical sign.

STEP 2

1. Express the coefficient as a square under the radical.
2. Combine the expressions under the radical.

STEP 3

Express the coefficient $2$ as a square under the radical.
$2 = \sqrt{4}$
So, $2 \sqrt{3}$ can be rewritten as:
$\sqrt{4} \times \sqrt{3}$

STEP 4

Combine the expressions under the radical using the property $\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}$ .
$\sqrt{4} \times \sqrt{3} = \sqrt{4 \times 3}$
$\sqrt{4 \times 3} = \sqrt{12}$
The entire radical form of $2 \sqrt{3}$ is:
$\boxed{\sqrt{12}}$

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