Solve (sqrt{50}*sqrt{2}):(sqrt{3+4})=

$$( \sqrt { 50 } \times \sqrt { 2 } ) : ( \sqrt { 3 + 4 } ) =$$

Evaluate

$$\frac{10\sqrt{7}}{7}\approx 3.77964473$$

Solution Steps

Factor 50=2\times 25. Rewrite the square root of the product \sqrt{2\times 25} as the product of square roots \sqrt{2}\sqrt{25}.

$$\frac{\sqrt{2}\sqrt{25}\sqrt{2}}{\sqrt{3+4}}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\frac{2\sqrt{25}}{\sqrt{3+4}}$$

Calculate the square root of 25 and get 5.

$$\frac{2\times 5}{\sqrt{3+4}}$$

Multiply 2 and 5 to get 10.

$$\frac{10}{\sqrt{3+4}}$$

Add 3 and 4 to get 7.

$$\frac{10}{\sqrt{7}}$$

Rationalize the denominator of \frac{10}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{10\sqrt{7}}{\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

$$\frac{10\sqrt{7}}{7}$$