Basic Math Examples

$65 = \sqrt{30 \cdot D \cdot 0.875 \cdot 1}$

Step 1

Rewrite the equation as $\sqrt{30 \cdot D \cdot 0.875 \cdot 1} = 65$ .

$\sqrt{30 \cdot D \cdot 0.875 \cdot 1} = 65$

Step 2

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

${\sqrt{30 \cdot D \cdot 0.875 \cdot 1}}^{2} = 65^{2}$

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 $\sqrt{30 \cdot D \cdot 0.875 \cdot 1}$ as ${(30 \cdot D \cdot 0.875 \cdot 1)}^{\frac{1}{2}}$ .

${({(30 \cdot D \cdot 0.875 \cdot 1)}^{\frac{1}{2}})}^{2} = 65^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${({(30 \cdot D \cdot 0.875 \cdot 1)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Multiply the exponents in ${({(30 \cdot D \cdot 0.875 \cdot 1)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1.1

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

${(30 \cdot D \cdot 0.875 \cdot 1)}^{\frac{1}{2} \cdot 2} = 65^{2}$

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.

${(30 \cdot D \cdot 0.875 \cdot 1)}^{\frac{1}{2} \cdot 2} = 65^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

${(30 \cdot D \cdot 0.875 \cdot 1)}^{1} = 65^{2}$

Step 3.2.1.2

Multiply $0.875$ by $30$ .

${(26.25 D \cdot 1)}^{1} = 65^{2}$

Step 3.2.1.3

Simplify.

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Step 3.2.1.3.1

Multiply $26.25$ by $1$ .

${(26.25 D)}^{1} = 65^{2}$

Step 3.2.1.3.2

Simplify.

$26.25 D = 65^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Raise $65$ to the power of $2$ .

$26.25 D = 4225$

Step 4

Divide each term in $26.25 D = 4225$ by $26.25$ and simplify.

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Step 4.1

Divide each term in $26.25 D = 4225$ by $26.25$ .

$\frac{26.25 D}{26.25} = \frac{4225}{26.25}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $26.25$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{26.25 D}{26.25} = \frac{4225}{26.25}$

Step 4.2.1.2

Divide $D$ by $1$ .

$D = \frac{4225}{26.25}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $4225$ by $26.25$ .

$D = 160.\overline{952380}$