Basic Math Examples

$\frac{11}{14} = \sqrt{d}$

Step 1

Rewrite the equation as $\sqrt{d} = \frac{11}{14}$ .

$\sqrt{d} = \frac{11}{14}$

Step 2

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{d}}^{2} = {(\frac{11}{14})}^{2}$

Step 3

Simplify each side of the equation.

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Step 3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{d}$ as $d^{\frac{1}{2}}$ .

${(d^{\frac{1}{2}})}^{2} = {(\frac{11}{14})}^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${(d^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Multiply the exponents in ${(d^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$d^{\frac{1}{2} \cdot 2} = {(\frac{11}{14})}^{2}$

Step 3.2.1.1.2

Cancel the common factor of $2$ .

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Step 3.2.1.1.2.1

Cancel the common factor.

$d^{\frac{1}{2} \cdot 2} = {(\frac{11}{14})}^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

$d^{1} = {(\frac{11}{14})}^{2}$

Step 3.2.1.2

Simplify.

$d = {(\frac{11}{14})}^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify ${(\frac{11}{14})}^{2}$ .

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Step 3.3.1.1

Apply the product rule to $\frac{11}{14}$ .

$d = \frac{11^{2}}{14^{2}}$

Step 3.3.1.2

Raise $11$ to the power of $2$ .

$d = \frac{121}{14^{2}}$

Step 3.3.1.3

Raise $14$ to the power of $2$ .

$d = \frac{121}{196}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$d = \frac{121}{196}$

Decimal Form:

$d = 0.61734693 \dots$