Math / Numbers & Operations

Question $\frac{\sqrt{6}}{4}+\frac{\sqrt{6}}{2}$

Studdy Solution

STEP 1

1. The expression $\frac{\sqrt{6}}{4} + \frac{\sqrt{6}}{2}$ involves basic arithmetic with fractions and square roots.
2. Simplification involves combining like terms by finding a common denominator.

STEP 2

1. Identify the common denominator for the fractions $\frac{\sqrt{6}}{4}$ and $\frac{\sqrt{6}}{2}$ .
2. Rewrite each fraction with the common denominator.
3. Add the fractions.
4. Simplify the resulting expression if possible.

STEP 3

Identify the common denominator for the fractions $\frac{\sqrt{6}}{4}$ and $\frac{\sqrt{6}}{2}$ .
The common denominator is $4$ .

STEP 4

Rewrite $\frac{\sqrt{6}}{2}$ with the common denominator $4$ .
$\frac{\sqrt{6}}{2} = \frac{\sqrt{6} \times 2}{2 \times 2} = \frac{2\sqrt{6}}{4}$

STEP 5

Add the fractions $\frac{\sqrt{6}}{4}$ and $\frac{2\sqrt{6}}{4}$ .
$\frac{\sqrt{6}}{4} + \frac{2\sqrt{6}}{4} = \frac{\sqrt{6} + 2\sqrt{6}}{4}$

STEP 6

Combine the terms in the numerator.
$\frac{\sqrt{6} + 2\sqrt{6}}{4} = \frac{3\sqrt{6}}{4}$
Therefore, the solution to $\frac{\sqrt{6}}{4} + \frac{\sqrt{6}}{2}$ is $\frac{3\sqrt{6}}{4}$ .

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Question $\frac{\sqrt{6}}{4}+\frac{\sqrt{6}}{2}$

Studdy Solution

STEP 1

1. The expression $\frac{\sqrt{6}}{4} + \frac{\sqrt{6}}{2}$ involves basic arithmetic with fractions and square roots.
2. Simplification involves combining like terms by finding a common denominator.

STEP 2

1. Identify the common denominator for the fractions $\frac{\sqrt{6}}{4}$ and $\frac{\sqrt{6}}{2}$ .
2. Rewrite each fraction with the common denominator.
3. Add the fractions.
4. Simplify the resulting expression if possible.

STEP 3

Identify the common denominator for the fractions $\frac{\sqrt{6}}{4}$ and $\frac{\sqrt{6}}{2}$ .
The common denominator is $4$ .

STEP 4

Rewrite $\frac{\sqrt{6}}{2}$ with the common denominator $4$ .
$\frac{\sqrt{6}}{2} = \frac{\sqrt{6} \times 2}{2 \times 2} = \frac{2\sqrt{6}}{4}$

STEP 5

Add the fractions $\frac{\sqrt{6}}{4}$ and $\frac{2\sqrt{6}}{4}$ .
$\frac{\sqrt{6}}{4} + \frac{2\sqrt{6}}{4} = \frac{\sqrt{6} + 2\sqrt{6}}{4}$

STEP 6

Combine the terms in the numerator.
$\frac{\sqrt{6} + 2\sqrt{6}}{4} = \frac{3\sqrt{6}}{4}$
Therefore, the solution to $\frac{\sqrt{6}}{4} + \frac{\sqrt{6}}{2}$ is $\frac{3\sqrt{6}}{4}$ .

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Question64+62\frac{\sqrt{6}}{4}+\frac{\sqrt{6}}{2}46​​+26​​

Studdy Solution

STEP 1

1. The expression 64+62\frac{\sqrt{6}}{4} + \frac{\sqrt{6}}{2}46​​+26​​ involves basic arithmetic with fractions and square roots.2. Simplification involves combining like terms by finding a common denominator.

STEP 2

1. Identify the common denominator for the fractions 64\frac{\sqrt{6}}{4}46​​ and 62\frac{\sqrt{6}}{2}26​​.2. Rewrite each fraction with the common denominator.3. Add the fractions.4. Simplify the resulting expression if possible.

STEP 3

Identify the common denominator for the fractions 64\frac{\sqrt{6}}{4}46​​ and 62\frac{\sqrt{6}}{2}26​​.The common denominator is 444.

STEP 4

Rewrite 62\frac{\sqrt{6}}{2}26​​ with the common denominator 444.62=6×22×2=264 \frac{\sqrt{6}}{2} = \frac{\sqrt{6} \times 2}{2 \times 2} = \frac{2\sqrt{6}}{4} 26​​=2×26​×2​=426​​

STEP 5

Add the fractions 64\frac{\sqrt{6}}{4}46​​ and 264\frac{2\sqrt{6}}{4}426​​.64+264=6+264 \frac{\sqrt{6}}{4} + \frac{2\sqrt{6}}{4} = \frac{\sqrt{6} + 2\sqrt{6}}{4} 46​​+426​​=46​+26​​

STEP 6

Combine the terms in the numerator.6+264=364 \frac{\sqrt{6} + 2\sqrt{6}}{4} = \frac{3\sqrt{6}}{4} 46​+26​​=436​​Therefore, the solution to 64+62\frac{\sqrt{6}}{4} + \frac{\sqrt{6}}{2}46​​+26​​ is 364\frac{3\sqrt{6}}{4}436​​.

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Question $\frac{\sqrt{6}}{4}+\frac{\sqrt{6}}{2}$

1. The expression $\frac{\sqrt{6}}{4} + \frac{\sqrt{6}}{2}$ involves basic arithmetic with fractions and square roots.
2. Simplification involves combining like terms by finding a common denominator.

1. Identify the common denominator for the fractions $\frac{\sqrt{6}}{4}$ and $\frac{\sqrt{6}}{2}$ .
2. Rewrite each fraction with the common denominator.
3. Add the fractions.
4. Simplify the resulting expression if possible.

Identify the common denominator for the fractions $\frac{\sqrt{6}}{4}$ and $\frac{\sqrt{6}}{2}$ .
The common denominator is $4$ .

Rewrite $\frac{\sqrt{6}}{2}$ with the common denominator $4$ .
$\frac{\sqrt{6}}{2} = \frac{\sqrt{6} \times 2}{2 \times 2} = \frac{2\sqrt{6}}{4}$

Add the fractions $\frac{\sqrt{6}}{4}$ and $\frac{2\sqrt{6}}{4}$ .
$\frac{\sqrt{6}}{4} + \frac{2\sqrt{6}}{4} = \frac{\sqrt{6} + 2\sqrt{6}}{4}$

Combine the terms in the numerator.
$\frac{\sqrt{6} + 2\sqrt{6}}{4} = \frac{3\sqrt{6}}{4}$
Therefore, the solution to $\frac{\sqrt{6}}{4} + \frac{\sqrt{6}}{2}$ is $\frac{3\sqrt{6}}{4}$ .