Basic Math Examples

$(3 \sqrt{7}, - 3 \sqrt{5})$ , $(9 \sqrt{7}, 7 \sqrt{5})$

Step 1

Use the distance formula to determine the distance between the two points.

$Distance = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$

Step 2

Substitute the actual values of the points into the distance formula.

$\sqrt{{(9 \sqrt{7} - 3 \sqrt{7})}^{2} + {(7 \sqrt{5} - (- 3 \sqrt{5}))}^{2}}$

Step 3

Simplify.

Tap for more steps...

Step 3.1

Subtract $3 \sqrt{7}$ from $9 \sqrt{7}$ .

$\sqrt{{(6 \sqrt{7})}^{2} + {(7 \sqrt{5} - (- 3 \sqrt{5}))}^{2}}$

Step 3.2

Simplify the expression.

Tap for more steps...

Step 3.2.1

Apply the product rule to $6 \sqrt{7}$ .

$\sqrt{6^{2} {\sqrt{7}}^{2} + {(7 \sqrt{5} - (- 3 \sqrt{5}))}^{2}}$

Step 3.2.2

Raise $6$ to the power of $2$ .

$\sqrt{36 {\sqrt{7}}^{2} + {(7 \sqrt{5} - (- 3 \sqrt{5}))}^{2}}$

Step 3.3

Rewrite ${\sqrt{7}}^{2}$ as $7$ .

Tap for more steps...

Step 3.3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7}$ as $7^{\frac{1}{2}}$ .

$\sqrt{36 {(7^{\frac{1}{2}})}^{2} + {(7 \sqrt{5} - (- 3 \sqrt{5}))}^{2}}$

Step 3.3.2

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

$\sqrt{36 \cdot 7^{\frac{1}{2} \cdot 2} + {(7 \sqrt{5} - (- 3 \sqrt{5}))}^{2}}$

Step 3.3.3

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

$\sqrt{36 \cdot 7^{\frac{2}{2}} + {(7 \sqrt{5} - (- 3 \sqrt{5}))}^{2}}$

Step 3.3.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.3.4.1

Cancel the common factor.

$\sqrt{36 \cdot 7^{\frac{2}{2}} + {(7 \sqrt{5} - (- 3 \sqrt{5}))}^{2}}$

Step 3.3.4.2

Rewrite the expression.

$\sqrt{36 \cdot 7^{1} + {(7 \sqrt{5} - (- 3 \sqrt{5}))}^{2}}$

Step 3.3.5

Evaluate the exponent.

$\sqrt{36 \cdot 7 + {(7 \sqrt{5} - (- 3 \sqrt{5}))}^{2}}$

Step 3.4

Multiply.

Tap for more steps...

Step 3.4.1

Multiply $36$ by $7$ .

$\sqrt{252 + {(7 \sqrt{5} - (- 3 \sqrt{5}))}^{2}}$

Step 3.4.2

Multiply $- 3$ by $- 1$ .

$\sqrt{252 + {(7 \sqrt{5} + 3 \sqrt{5})}^{2}}$

Step 3.5

Add $7 \sqrt{5}$ and $3 \sqrt{5}$ .

$\sqrt{252 + {(10 \sqrt{5})}^{2}}$

Step 3.6

Simplify the expression.

Tap for more steps...

Step 3.6.1

Apply the product rule to $10 \sqrt{5}$ .

$\sqrt{252 + 10^{2} {\sqrt{5}}^{2}}$

Step 3.6.2

Raise $10$ to the power of $2$ .

$\sqrt{252 + 100 {\sqrt{5}}^{2}}$

Step 3.7

Rewrite ${\sqrt{5}}^{2}$ as $5$ .

Tap for more steps...

Step 3.7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

$\sqrt{252 + 100 {(5^{\frac{1}{2}})}^{2}}$

Step 3.7.2

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

$\sqrt{252 + 100 \cdot 5^{\frac{1}{2} \cdot 2}}$

Step 3.7.3

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

$\sqrt{252 + 100 \cdot 5^{\frac{2}{2}}}$

Step 3.7.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.7.4.1

Cancel the common factor.

$\sqrt{252 + 100 \cdot 5^{\frac{2}{2}}}$

Step 3.7.4.2

Rewrite the expression.

$\sqrt{252 + 100 \cdot 5^{1}}$

Step 3.7.5

Evaluate the exponent.

$\sqrt{252 + 100 \cdot 5}$

Step 3.8

Simplify the expression.

Tap for more steps...

Step 3.8.1

Multiply $100$ by $5$ .

$\sqrt{252 + 500}$

Step 3.8.2

Add $252$ and $500$ .

$\sqrt{752}$

Step 3.9

Rewrite $752$ as $4^{2} \cdot 47$ .

Tap for more steps...

Step 3.9.1

Factor $16$ out of $752$ .

$\sqrt{16 (47)}$

Step 3.9.2

Rewrite $16$ as $4^{2}$ .

$\sqrt{4^{2} \cdot 47}$

Step 3.10

Pull terms out from under the radical.

$4 \sqrt{47}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt{47}$

Decimal Form:

$27.42261840 \dots$

Step 5