Basic Math Examples

$4.2 \div \sqrt{40}$

Step 1

Rewrite the division as a fraction.

$\frac{4.2}{\sqrt{40}}$

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

Rewrite $40$ as $2^{2} \cdot 10$ .

Tap for more steps...

Step 2.1.1

Factor $4$ out of $40$ .

$\frac{4.2}{\sqrt{4 (10)}}$

Step 2.1.2

Rewrite $4$ as $2^{2}$ .

$\frac{4.2}{\sqrt{2^{2} \cdot 10}}$

Step 2.2

Pull terms out from under the radical.

$\frac{4.2}{2 \sqrt{10}}$

Step 3

Multiply $\frac{4.2}{2 \sqrt{10}}$ by $\frac{\sqrt{10}}{\sqrt{10}}$ .

$\frac{4.2}{2 \sqrt{10}} \cdot \frac{\sqrt{10}}{\sqrt{10}}$

Step 4

Combine and simplify the denominator.

Tap for more steps...

Step 4.1

Multiply $\frac{4.2}{2 \sqrt{10}}$ by $\frac{\sqrt{10}}{\sqrt{10}}$ .

$\frac{4.2 \sqrt{10}}{2 \sqrt{10} \sqrt{10}}$

Step 4.2

Move $\sqrt{10}$ .

$\frac{4.2 \sqrt{10}}{2 (\sqrt{10} \sqrt{10})}$

Step 4.3

Raise $\sqrt{10}$ to the power of $1$ .

$\frac{4.2 \sqrt{10}}{2 ({\sqrt{10}}^{1} \sqrt{10})}$

Step 4.4

Raise $\sqrt{10}$ to the power of $1$ .

$\frac{4.2 \sqrt{10}}{2 ({\sqrt{10}}^{1} {\sqrt{10}}^{1})}$

Step 4.5

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{4.2 \sqrt{10}}{2 {\sqrt{10}}^{1 + 1}}$

Step 4.6

Add $1$ and $1$ .

$\frac{4.2 \sqrt{10}}{2 {\sqrt{10}}^{2}}$

Step 4.7

Rewrite ${\sqrt{10}}^{2}$ as $10$ .

Tap for more steps...

Step 4.7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{10}$ as $10^{\frac{1}{2}}$ .

$\frac{4.2 \sqrt{10}}{2 {(10^{\frac{1}{2}})}^{2}}$

Step 4.7.2

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

$\frac{4.2 \sqrt{10}}{2 \cdot 10^{\frac{1}{2} \cdot 2}}$

Step 4.7.3

Combine $\frac{1}{2}$ and $2$ .

$\frac{4.2 \sqrt{10}}{2 \cdot 10^{\frac{2}{2}}}$

Step 4.7.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.7.4.1

Cancel the common factor.

$\frac{4.2 \sqrt{10}}{2 \cdot 10^{\frac{2}{2}}}$

Step 4.7.4.2

Rewrite the expression.

$\frac{4.2 \sqrt{10}}{2 \cdot 10^{1}}$

Step 4.7.5

Evaluate the exponent.

$\frac{4.2 \sqrt{10}}{2 \cdot 10}$

Step 5

Multiply $4.2$ by $\sqrt{10}$ .

$\frac{13.28156617}{2 \cdot 10}$

Step 6

Simplify the expression.

Tap for more steps...

Step 6.1

Multiply $2$ by $10$ .

$\frac{13.28156617}{20}$

Step 6.2

Divide $13.28156617$ by $20$ .

$0.6640783$