Math / Numbers & Operations

Question $\frac{\sqrt{3}}{2}+\frac{\sqrt{3}}{2}$

Studdy Solution

STEP 1

What is this asking? We're adding two identical square roots!
How simple is that?! Watch out! Don't accidentally multiply the square roots.
We are adding them.

STEP 2

1. Simplify the expression

STEP 3

We have two identical terms, both equal to $\frac{\sqrt{3}}{2}$ , and we're adding them together.
We can rewrite this as a multiplication!
This is like saying "one apple plus one apple" is the same as "two apples." So, we have:
$\frac{\sqrt{3}}{2} + \frac{\sqrt{3}}{2} = 2 \cdot \frac{\sqrt{3}}{2}$

STEP 4

We're multiplying $2$ by the fraction $\frac{\sqrt{3}}{2}$ .
Remember that $2$ is really $\frac{2}{1}$ , so we have:
$2 \cdot \frac{\sqrt{3}}{2} = \frac{2}{1} \cdot \frac{\sqrt{3}}{2}$

STEP 5

When multiplying fractions, we multiply the numerators together and the denominators together.
Let's do it:
$\frac{2}{1} \cdot \frac{\sqrt{3}}{2} = \frac{2 \cdot \sqrt{3}}{1 \cdot 2}$

STEP 6

Look at the fraction $\frac{2 \cdot \sqrt{3}}{1 \cdot 2}$ .
Both the numerator and the denominator have a factor of 2.
We can divide both the numerator and denominator by $\bf{2}$ to simplify the fraction.
Remember that dividing by $2$ is the same as multiplying by $\frac{1}{2}$ , so we have:
$\frac{2 \cdot \sqrt{3}}{2} \cdot \frac{\frac{1}{2}}{\frac{1}{2}} = \frac{1 \cdot \sqrt{3}}{1}$

STEP 7

Anything divided by $1$ is just itself, so we have:
$\frac{1 \cdot \sqrt{3}}{1} = \sqrt{3}$

STEP 8

Our final answer is $\sqrt{3}$ !

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