Basic Math Examples

$10 \sqrt{9 M} = 60$

Step 1

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

${(10 \sqrt{9 M})}^{2} = 60^{2}$

Step 2

Simplify each side of the equation.

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Step 2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{9 M}$ as ${(9 M)}^{\frac{1}{2}}$ .

${(10 {(9 M)}^{\frac{1}{2}})}^{2} = 60^{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify ${(10 {(9 M)}^{\frac{1}{2}})}^{2}$ .

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Step 2.2.1.1

Simplify the expression.

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Step 2.2.1.1.1

Apply the product rule to $9 M$ .

${(10 (9^{\frac{1}{2}} M^{\frac{1}{2}}))}^{2} = 60^{2}$

Step 2.2.1.1.2

Rewrite $9$ as $3^{2}$ .

${(10 ({(3^{2})}^{\frac{1}{2}} M^{\frac{1}{2}}))}^{2} = 60^{2}$

Step 2.2.1.1.3

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

${(10 (3^{2 (\frac{1}{2})} M^{\frac{1}{2}}))}^{2} = 60^{2}$

Step 2.2.1.2

Cancel the common factor of $2$ .

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Step 2.2.1.2.1

Cancel the common factor.

${(10 (3^{2 (\frac{1}{2})} M^{\frac{1}{2}}))}^{2} = 60^{2}$

Step 2.2.1.2.2

Rewrite the expression.

${(10 (3^{1} M^{\frac{1}{2}}))}^{2} = 60^{2}$

Step 2.2.1.3

Evaluate the exponent.

${(10 (3 M^{\frac{1}{2}}))}^{2} = 60^{2}$

Step 2.2.1.4

Multiply $3$ by $10$ .

${(30 M^{\frac{1}{2}})}^{2} = 60^{2}$

Step 2.2.1.5

Apply the product rule to $30 M^{\frac{1}{2}}$ .

$30^{2} {(M^{\frac{1}{2}})}^{2} = 60^{2}$

Step 2.2.1.6

Raise $30$ to the power of $2$ .

$900 {(M^{\frac{1}{2}})}^{2} = 60^{2}$

Step 2.2.1.7

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

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Step 2.2.1.7.1

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

$900 M^{\frac{1}{2} \cdot 2} = 60^{2}$

Step 2.2.1.7.2

Cancel the common factor of $2$ .

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Step 2.2.1.7.2.1

Cancel the common factor.

$900 M^{\frac{1}{2} \cdot 2} = 60^{2}$

Step 2.2.1.7.2.2

Rewrite the expression.

$900 M^{1} = 60^{2}$

Step 2.2.1.8

Simplify.

$900 M = 60^{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

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

$900 M = 3600$

Step 3

Divide each term in $900 M = 3600$ by $900$ and simplify.

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Step 3.1

Divide each term in $900 M = 3600$ by $900$ .

$\frac{900 M}{900} = \frac{3600}{900}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $900$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{900 M}{900} = \frac{3600}{900}$

Step 3.2.1.2

Divide $M$ by $1$ .

$M = \frac{3600}{900}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $3600$ by $900$ .

$M = 4$