Divide (2 square root of 30-3 square root of 70)/( square root of 10)

$\frac{2 \sqrt{30} - 3 \sqrt{70}}{\sqrt{10}}$

Step 1

Multiply $\frac{2 \sqrt{30} - 3 \sqrt{70}}{\sqrt{10}}$ by $\frac{\sqrt{10}}{\sqrt{10}}$ .

$\frac{2 \sqrt{30} - 3 \sqrt{70}}{\sqrt{10}} \cdot \frac{\sqrt{10}}{\sqrt{10}}$

Step 2

Combine and simplify the denominator.

Multiply $\frac{2 \sqrt{30} - 3 \sqrt{70}}{\sqrt{10}}$ by $\frac{\sqrt{10}}{\sqrt{10}}$ .

$\frac{(2 \sqrt{30} - 3 \sqrt{70}) \sqrt{10}}{\sqrt{10} \sqrt{10}}$

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

$\frac{(2 \sqrt{30} - 3 \sqrt{70}) \sqrt{10}}{{\sqrt{10}}^{1} \sqrt{10}}$

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

$\frac{(2 \sqrt{30} - 3 \sqrt{70}) \sqrt{10}}{{\sqrt{10}}^{1} {\sqrt{10}}^{1}}$

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

$\frac{(2 \sqrt{30} - 3 \sqrt{70}) \sqrt{10}}{{\sqrt{10}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{(2 \sqrt{30} - 3 \sqrt{70}) \sqrt{10}}{{\sqrt{10}}^{2}}$

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

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

$\frac{(2 \sqrt{30} - 3 \sqrt{70}) \sqrt{10}}{{(10^{\frac{1}{2}})}^{2}}$

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

$\frac{(2 \sqrt{30} - 3 \sqrt{70}) \sqrt{10}}{10^{\frac{1}{2} \cdot 2}}$

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

$\frac{(2 \sqrt{30} - 3 \sqrt{70}) \sqrt{10}}{10^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{(2 \sqrt{30} - 3 \sqrt{70}) \sqrt{10}}{10^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{(2 \sqrt{30} - 3 \sqrt{70}) \sqrt{10}}{10^{1}}$

Evaluate the exponent.

$\frac{(2 \sqrt{30} - 3 \sqrt{70}) \sqrt{10}}{10}$

Step 3

Apply the distributive property.

$\frac{2 \sqrt{30} \sqrt{10} - 3 \sqrt{70} \sqrt{10}}{10}$

Step 4

Multiply $2 \sqrt{30} \sqrt{10}$ .

Combine using the product rule for radicals.

$\frac{2 \sqrt{10 \cdot 30} - 3 \sqrt{70} \sqrt{10}}{10}$

Multiply $10$ by $30$ .

$\frac{2 \sqrt{300} - 3 \sqrt{70} \sqrt{10}}{10}$

Step 5

Multiply $- 3 \sqrt{70} \sqrt{10}$ .

Combine using the product rule for radicals.

$\frac{2 \sqrt{300} - 3 \sqrt{10 \cdot 70}}{10}$

Multiply $10$ by $70$ .

$\frac{2 \sqrt{300} - 3 \sqrt{700}}{10}$

Step 6

Simplify each term.

Rewrite $300$ as $10^{2} \cdot 3$ .

Factor $100$ out of $300$ .

$\frac{2 \sqrt{100 (3)} - 3 \sqrt{700}}{10}$

Rewrite $100$ as $10^{2}$ .

$\frac{2 \sqrt{10^{2} \cdot 3} - 3 \sqrt{700}}{10}$

Pull terms out from under the radical.

$\frac{2 (10 \sqrt{3}) - 3 \sqrt{700}}{10}$

Multiply $10$ by $2$ .

$\frac{20 \sqrt{3} - 3 \sqrt{700}}{10}$

Rewrite $700$ as $10^{2} \cdot 7$ .

Factor $100$ out of $700$ .

$\frac{20 \sqrt{3} - 3 \sqrt{100 (7)}}{10}$

Rewrite $100$ as $10^{2}$ .

$\frac{20 \sqrt{3} - 3 \sqrt{10^{2} \cdot 7}}{10}$

Pull terms out from under the radical.

$\frac{20 \sqrt{3} - 3 (10 \sqrt{7})}{10}$

Multiply $10$ by $- 3$ .

$\frac{20 \sqrt{3} - 30 \sqrt{7}}{10}$

Step 7

Cancel the common factor of $20 \sqrt{3} - 30 \sqrt{7}$ and $10$ .

Factor $10$ out of $20 \sqrt{3}$ .

$\frac{10 (2 \sqrt{3}) - 30 \sqrt{7}}{10}$

Factor $10$ out of $- 30 \sqrt{7}$ .

$\frac{10 (2 \sqrt{3}) + 10 (- 3 \sqrt{7})}{10}$

Factor $10$ out of $10 (2 \sqrt{3}) + 10 (- 3 \sqrt{7})$ .

$\frac{10 (2 \sqrt{3} - 3 \sqrt{7})}{10}$

Cancel the common factors.

Factor $10$ out of $10$ .

$\frac{10 (2 \sqrt{3} - 3 \sqrt{7})}{10 (1)}$

Cancel the common factor.

$\frac{10 (2 \sqrt{3} - 3 \sqrt{7})}{10 \cdot 1}$

Rewrite the expression.

$\frac{2 \sqrt{3} - 3 \sqrt{7}}{1}$

Divide $2 \sqrt{3} - 3 \sqrt{7}$ by $1$ .

$2 \sqrt{3} - 3 \sqrt{7}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{3} - 3 \sqrt{7}$

Decimal Form:

$- 4.47315231 \dots$

Divide (2 square root of 30-3 square root of 70)/( square root of 10)

Related Questions

Support LCMGCF.com by disabling your adblocker.