Basic Math Examples

$60 = \sqrt{21 d}$

Step 1

Rewrite the equation as $\sqrt{21 d} = 60$ .

$\sqrt{21 d} = 60$

Step 2

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

${\sqrt{21 d}}^{2} = 60^{2}$

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 $\sqrt{21 d}$ as ${(21 d)}^{\frac{1}{2}}$ .

${({(21 d)}^{\frac{1}{2}})}^{2} = 60^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${({(21 d)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Multiply the exponents in ${({(21 d)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1.1

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

${(21 d)}^{\frac{1}{2} \cdot 2} = 60^{2}$

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.

${(21 d)}^{\frac{1}{2} \cdot 2} = 60^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

${(21 d)}^{1} = 60^{2}$

Step 3.2.1.2

Simplify.

$21 d = 60^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Raise $60$ to the power of $2$ .

$21 d = 3600$

Step 4

Divide each term in $21 d = 3600$ by $21$ and simplify.

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Step 4.1

Divide each term in $21 d = 3600$ by $21$ .

$\frac{21 d}{21} = \frac{3600}{21}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $21$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{21 d}{21} = \frac{3600}{21}$

Step 4.2.1.2

Divide $d$ by $1$ .

$d = \frac{3600}{21}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Cancel the common factor of $3600$ and $21$ .

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Step 4.3.1.1

Factor $3$ out of $3600$ .

$d = \frac{3 (1200)}{21}$

Step 4.3.1.2

Cancel the common factors.

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Step 4.3.1.2.1

Factor $3$ out of $21$ .

$d = \frac{3 \cdot 1200}{3 \cdot 7}$

Step 4.3.1.2.2

Cancel the common factor.

$d = \frac{3 \cdot 1200}{3 \cdot 7}$

Step 4.3.1.2.3

Rewrite the expression.

$d = \frac{1200}{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$d = \frac{1200}{7}$

Decimal Form:

$d = 171.42857142 \dots$

Mixed Number Form:

$d = 171 \frac{3}{7}$