Basic Math Examples

$\sqrt{3} = k \sqrt{7} \sqrt{5}$

Step 1

Rewrite the equation as $k \sqrt{7} \sqrt{5} = \sqrt{3}$ .

$k \sqrt{7} \sqrt{5} = \sqrt{3}$

Step 2

Simplify.

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Step 2.1

Combine using the product rule for radicals.

$k \sqrt{5 \cdot 7} = \sqrt{3}$

Step 2.2

Multiply $5$ by $7$ .

$k \sqrt{35} = \sqrt{3}$

Step 3

Divide each term in $k \sqrt{35} = \sqrt{3}$ by $\sqrt{35}$ and simplify.

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Step 3.1

Divide each term in $k \sqrt{35} = \sqrt{3}$ by $\sqrt{35}$ .

$\frac{k \sqrt{35}}{\sqrt{35}} = \frac{\sqrt{3}}{\sqrt{35}}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $\sqrt{35}$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{k \sqrt{35}}{\sqrt{35}} = \frac{\sqrt{3}}{\sqrt{35}}$

Step 3.2.1.2

Divide $k$ by $1$ .

$k = \frac{\sqrt{3}}{\sqrt{35}}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply $\frac{\sqrt{3}}{\sqrt{35}}$ by $\frac{\sqrt{35}}{\sqrt{35}}$ .

$k = \frac{\sqrt{3}}{\sqrt{35}} \cdot \frac{\sqrt{35}}{\sqrt{35}}$

Step 3.3.2

Combine and simplify the denominator.

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Step 3.3.2.1

Multiply $\frac{\sqrt{3}}{\sqrt{35}}$ by $\frac{\sqrt{35}}{\sqrt{35}}$ .

$k = \frac{\sqrt{3} \sqrt{35}}{\sqrt{35} \sqrt{35}}$

Step 3.3.2.2

Raise $\sqrt{35}$ to the power of $1$ .

$k = \frac{\sqrt{3} \sqrt{35}}{{\sqrt{35}}^{1} \sqrt{35}}$

Step 3.3.2.3

Raise $\sqrt{35}$ to the power of $1$ .

$k = \frac{\sqrt{3} \sqrt{35}}{{\sqrt{35}}^{1} {\sqrt{35}}^{1}}$

Step 3.3.2.4

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

$k = \frac{\sqrt{3} \sqrt{35}}{{\sqrt{35}}^{1 + 1}}$

Step 3.3.2.5

Add $1$ and $1$ .

$k = \frac{\sqrt{3} \sqrt{35}}{{\sqrt{35}}^{2}}$

Step 3.3.2.6

Rewrite ${\sqrt{35}}^{2}$ as $35$ .

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Step 3.3.2.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{35}$ as $35^{\frac{1}{2}}$ .

$k = \frac{\sqrt{3} \sqrt{35}}{{(35^{\frac{1}{2}})}^{2}}$

Step 3.3.2.6.2

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

$k = \frac{\sqrt{3} \sqrt{35}}{35^{\frac{1}{2} \cdot 2}}$

Step 3.3.2.6.3

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

$k = \frac{\sqrt{3} \sqrt{35}}{35^{\frac{2}{2}}}$

Step 3.3.2.6.4

Cancel the common factor of $2$ .

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Step 3.3.2.6.4.1

Cancel the common factor.

$k = \frac{\sqrt{3} \sqrt{35}}{35^{\frac{2}{2}}}$

Step 3.3.2.6.4.2

Rewrite the expression.

$k = \frac{\sqrt{3} \sqrt{35}}{35^{1}}$

Step 3.3.2.6.5

Evaluate the exponent.

$k = \frac{\sqrt{3} \sqrt{35}}{35}$

Step 3.3.3

Simplify the numerator.

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Step 3.3.3.1

Combine using the product rule for radicals.

$k = \frac{\sqrt{3 \cdot 35}}{35}$

Step 3.3.3.2

Multiply $3$ by $35$ .

$k = \frac{\sqrt{105}}{35}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$k = \frac{\sqrt{105}}{35}$

Decimal Form:

$k = 0.29277002 \dots$