QuestionSimplify the expression: $\frac{1}{\sqrt{0+14}+\sqrt{14}}$

Studdy Solution

STEP 1

Assumptions1. We are given the expression $\frac{1}{\sqrt{0+14}+\sqrt{14}}$ . We need to simplify this expression

STEP 2

First, simplify the expression inside the square root.
$\sqrt{0+14} = \sqrt{14}$ So, the expression becomes $\frac{1}{\sqrt{14}+\sqrt{14}}$

STEP 3

Combine the like terms under the square root.
$\frac{1}{2\sqrt{14}}$

STEP 4

To simplify further, we can rationalize the denominator. We do this by multiplying both the numerator and the denominator by the conjugate of the denominator. The conjugate of $2\sqrt{14}$ is $2\sqrt{14}$ .
$\frac{1}{2\sqrt{14}} \times \frac{2\sqrt{14}}{2\sqrt{14}}$

STEP 5

Multiply the numerators together and the denominators together.
$\frac{2\sqrt{14}}{4 \times14}$

STEP 6

implify the denominator.
$\frac{2\sqrt{14}}{56}$

STEP 7

Reduce the fraction by dividing both the numerator and the denominator by2.
$\frac{\sqrt{14}}{28}$ This is the simplified form of the given expression.

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QuestionSimplify the expression: $\frac{1}{\sqrt{0+14}+\sqrt{14}}$

Studdy Solution

STEP 1

Assumptions1. We are given the expression $\frac{1}{\sqrt{0+14}+\sqrt{14}}$ . We need to simplify this expression

STEP 2

First, simplify the expression inside the square root.
$\sqrt{0+14} = \sqrt{14}$ So, the expression becomes $\frac{1}{\sqrt{14}+\sqrt{14}}$

STEP 3

Combine the like terms under the square root.
$\frac{1}{2\sqrt{14}}$

STEP 4

To simplify further, we can rationalize the denominator. We do this by multiplying both the numerator and the denominator by the conjugate of the denominator. The conjugate of $2\sqrt{14}$ is $2\sqrt{14}$ .
$\frac{1}{2\sqrt{14}} \times \frac{2\sqrt{14}}{2\sqrt{14}}$

STEP 5

Multiply the numerators together and the denominators together.
$\frac{2\sqrt{14}}{4 \times14}$

STEP 6

implify the denominator.
$\frac{2\sqrt{14}}{56}$

STEP 7

Reduce the fraction by dividing both the numerator and the denominator by2.
$\frac{\sqrt{14}}{28}$ This is the simplified form of the given expression.

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QuestionSimplify the expression: 10+14+14\frac{1}{\sqrt{0+14}+\sqrt{14}}0+14​+14​1​

Studdy Solution

STEP 1

Assumptions1. We are given the expression 10+14+14\frac{1}{\sqrt{0+14}+\sqrt{14}}0+14​+14​1​. We need to simplify this expression

STEP 2

First, simplify the expression inside the square root.0+14=14\sqrt{0+14} = \sqrt{14}0+14​=14​So, the expression becomes114+14\frac{1}{\sqrt{14}+\sqrt{14}}14​+14​1​

STEP 3

Combine the like terms under the square root.1214\frac{1}{2\sqrt{14}}214​1​

STEP 4

STEP 5

Multiply the numerators together and the denominators together.2144×14\frac{2\sqrt{14}}{4 \times14}4×14214​​

STEP 6

implify the denominator.21456\frac{2\sqrt{14}}{56}56214​​

STEP 7

Reduce the fraction by dividing both the numerator and the denominator by2.1428\frac{\sqrt{14}}{28}2814​​This is the simplified form of the given expression.

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QuestionSimplify the expression: $\frac{1}{\sqrt{0+14}+\sqrt{14}}$

Assumptions1. We are given the expression $\frac{1}{\sqrt{0+14}+\sqrt{14}}$ . We need to simplify this expression

First, simplify the expression inside the square root.
$\sqrt{0+14} = \sqrt{14}$ So, the expression becomes $\frac{1}{\sqrt{14}+\sqrt{14}}$

Combine the like terms under the square root.
$\frac{1}{2\sqrt{14}}$

Multiply the numerators together and the denominators together.
$\frac{2\sqrt{14}}{4 \times14}$

implify the denominator.
$\frac{2\sqrt{14}}{56}$

Reduce the fraction by dividing both the numerator and the denominator by2.
$\frac{\sqrt{14}}{28}$ This is the simplified form of the given expression.