Simplify 2/( square root of 42)

$\frac{2}{\sqrt{42}}$

Step 1

Multiply $\frac{2}{\sqrt{42}}$ by $\frac{\sqrt{42}}{\sqrt{42}}$ .

$\frac{2}{\sqrt{42}} \cdot \frac{\sqrt{42}}{\sqrt{42}}$

Step 2

Combine and simplify the denominator.

Multiply $\frac{2}{\sqrt{42}}$ by $\frac{\sqrt{42}}{\sqrt{42}}$ .

$\frac{2 \sqrt{42}}{\sqrt{42} \sqrt{42}}$

Raise $\sqrt{42}$ to the power of $1$ .

$\frac{2 \sqrt{42}}{{\sqrt{42}}^{1} \sqrt{42}}$

Raise $\sqrt{42}$ to the power of $1$ .

$\frac{2 \sqrt{42}}{{\sqrt{42}}^{1} {\sqrt{42}}^{1}}$

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

$\frac{2 \sqrt{42}}{{\sqrt{42}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{2 \sqrt{42}}{{\sqrt{42}}^{2}}$

Rewrite ${\sqrt{42}}^{2}$ as $42$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{42}$ as $42^{\frac{1}{2}}$ .

$\frac{2 \sqrt{42}}{{(42^{\frac{1}{2}})}^{2}}$

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

$\frac{2 \sqrt{42}}{42^{\frac{1}{2} \cdot 2}}$

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

$\frac{2 \sqrt{42}}{42^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 \sqrt{42}}{42^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{2 \sqrt{42}}{42^{1}}$

Evaluate the exponent.

$\frac{2 \sqrt{42}}{42}$

Step 3

Cancel the common factor of $2$ and $42$ .

Factor $2$ out of $2 \sqrt{42}$ .

$\frac{2 (\sqrt{42})}{42}$

Cancel the common factors.

Factor $2$ out of $42$ .

$\frac{2 \sqrt{42}}{2 \cdot 21}$

Cancel the common factor.

$\frac{2 \sqrt{42}}{2 \cdot 21}$

Rewrite the expression.

$\frac{\sqrt{42}}{21}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{42}}{21}$

Decimal Form:

$0.30860669 \dots$

Simplify 2/( square root of 42)

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