Simplify (5 square root of 18-2 square root of 50)/( square root of 50)

$\frac{5 \sqrt{18} - 2 \sqrt{50}}{\sqrt{50}}$

Step 1

Simplify the numerator.

Rewrite $18$ as $3^{2} \cdot 2$ .

Factor $9$ out of $18$ .

$\frac{5 \sqrt{9 (2)} - 2 \sqrt{50}}{\sqrt{50}}$

Rewrite $9$ as $3^{2}$ .

$\frac{5 \sqrt{3^{2} \cdot 2} - 2 \sqrt{50}}{\sqrt{50}}$

Pull terms out from under the radical.

$\frac{5 (3 \sqrt{2}) - 2 \sqrt{50}}{\sqrt{50}}$

Multiply $3$ by $5$ .

$\frac{15 \sqrt{2} - 2 \sqrt{50}}{\sqrt{50}}$

Rewrite $50$ as $5^{2} \cdot 2$ .

Factor $25$ out of $50$ .

$\frac{15 \sqrt{2} - 2 \sqrt{25 (2)}}{\sqrt{50}}$

Rewrite $25$ as $5^{2}$ .

$\frac{15 \sqrt{2} - 2 \sqrt{5^{2} \cdot 2}}{\sqrt{50}}$

Pull terms out from under the radical.

$\frac{15 \sqrt{2} - 2 (5 \sqrt{2})}{\sqrt{50}}$

Multiply $5$ by $- 2$ .

$\frac{15 \sqrt{2} - 10 \sqrt{2}}{\sqrt{50}}$

Subtract $10 \sqrt{2}$ from $15 \sqrt{2}$ .

$\frac{5 \sqrt{2}}{\sqrt{50}}$

Step 2

Simplify the denominator.

Rewrite $50$ as $5^{2} \cdot 2$ .

Factor $25$ out of $50$ .

$\frac{5 \sqrt{2}}{\sqrt{25 (2)}}$

Rewrite $25$ as $5^{2}$ .

$\frac{5 \sqrt{2}}{\sqrt{5^{2} \cdot 2}}$

Pull terms out from under the radical.

$\frac{5 \sqrt{2}}{5 \sqrt{2}}$

Step 3

Reduce the expression by cancelling the common factors.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 \sqrt{2}}{5 \sqrt{2}}$

Rewrite the expression.

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

Cancel the common factor of $\sqrt{2}$ .

Cancel the common factor.

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

Rewrite the expression.

$1$