QuestionSimplify the expression $\frac{(3+\sqrt{6})}{\sqrt{3}}$ .

Studdy Solution

STEP 1

Assumptions1. We are asked to simplify the expression $\frac{(3+\sqrt{6})}{\sqrt{3}}$ . We can use the property of rationalizing the denominator to simplify the expression

STEP 2

The first step in simplifying this expression is to rationalize the denominator. We do this by multiplying the numerator and the denominator by the conjugate of the denominator. In this case, the conjugate of $\sqrt{}$ is $\sqrt{}$ .
$\frac{(+\sqrt{6})}{\sqrt{}} \times \frac{\sqrt{}}{\sqrt{}}$

STEP 3

Multiply the numerator and the denominator.
$\frac{(3+\sqrt{6})\sqrt{3}}{3}$

STEP 4

istribute the $\sqrt{3}$ in the numerator.
$\frac{3\sqrt{3}+\sqrt{18}}{3}$

STEP 5

implify the square root in the numerator.
$\frac{3\sqrt{3}+3\sqrt{2}}{3}$

STEP 6

Factor out a3 from the numerator.
$\frac{3(\sqrt{3}+\sqrt{2})}{3}$

STEP 7

Cancel out the3 in the numerator and the denominator.
$\sqrt{3}+\sqrt{2}$ So, the simplified form of $\frac{(3+\sqrt{6})}{\sqrt{3}}$ is $\sqrt{3}+\sqrt{2}$ .

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QuestionSimplify the expression $\frac{(3+\sqrt{6})}{\sqrt{3}}$ .

Studdy Solution

STEP 1

Assumptions1. We are asked to simplify the expression $\frac{(3+\sqrt{6})}{\sqrt{3}}$ . We can use the property of rationalizing the denominator to simplify the expression

STEP 2

The first step in simplifying this expression is to rationalize the denominator. We do this by multiplying the numerator and the denominator by the conjugate of the denominator. In this case, the conjugate of $\sqrt{}$ is $\sqrt{}$ .
$\frac{(+\sqrt{6})}{\sqrt{}} \times \frac{\sqrt{}}{\sqrt{}}$

STEP 3

Multiply the numerator and the denominator.
$\frac{(3+\sqrt{6})\sqrt{3}}{3}$

STEP 4

istribute the $\sqrt{3}$ in the numerator.
$\frac{3\sqrt{3}+\sqrt{18}}{3}$

STEP 5

implify the square root in the numerator.
$\frac{3\sqrt{3}+3\sqrt{2}}{3}$

STEP 6

Factor out a3 from the numerator.
$\frac{3(\sqrt{3}+\sqrt{2})}{3}$

STEP 7

Cancel out the3 in the numerator and the denominator.
$\sqrt{3}+\sqrt{2}$ So, the simplified form of $\frac{(3+\sqrt{6})}{\sqrt{3}}$ is $\sqrt{3}+\sqrt{2}$ .

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QuestionSimplify the expression (3+6)3\frac{(3+\sqrt{6})}{\sqrt{3}}3​(3+6​)​.

Studdy Solution

STEP 1

Assumptions1. We are asked to simplify the expression (3+6)3\frac{(3+\sqrt{6})}{\sqrt{3}}3​(3+6​)​ . We can use the property of rationalizing the denominator to simplify the expression

STEP 2

STEP 3

Multiply the numerator and the denominator.(3+6)33\frac{(3+\sqrt{6})\sqrt{3}}{3}3(3+6​)3​​

STEP 4

istribute the 3\sqrt{3}3​ in the numerator.33+183\frac{3\sqrt{3}+\sqrt{18}}{3}333​+18​​

STEP 5

implify the square root in the numerator.33+323\frac{3\sqrt{3}+3\sqrt{2}}{3}333​+32​​

STEP 6

Factor out a3 from the numerator.3(3+2)3\frac{3(\sqrt{3}+\sqrt{2})}{3}33(3​+2​)​

STEP 7

Cancel out the3 in the numerator and the denominator.3+2\sqrt{3}+\sqrt{2}3​+2​So, the simplified form of (3+6)3\frac{(3+\sqrt{6})}{\sqrt{3}}3​(3+6​)​ is 3+2\sqrt{3}+\sqrt{2}3​+2​.

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QuestionSimplify the expression $\frac{(3+\sqrt{6})}{\sqrt{3}}$ .

Assumptions1. We are asked to simplify the expression $\frac{(3+\sqrt{6})}{\sqrt{3}}$ . We can use the property of rationalizing the denominator to simplify the expression

Multiply the numerator and the denominator.
$\frac{(3+\sqrt{6})\sqrt{3}}{3}$

istribute the $\sqrt{3}$ in the numerator.
$\frac{3\sqrt{3}+\sqrt{18}}{3}$

implify the square root in the numerator.
$\frac{3\sqrt{3}+3\sqrt{2}}{3}$

Factor out a3 from the numerator.
$\frac{3(\sqrt{3}+\sqrt{2})}{3}$

Cancel out the3 in the numerator and the denominator.
$\sqrt{3}+\sqrt{2}$ So, the simplified form of $\frac{(3+\sqrt{6})}{\sqrt{3}}$ is $\sqrt{3}+\sqrt{2}$ .