Solve 3sqrt{frac{3.5sqrt{4}}{10sqrt{16}}}

$$3 \sqrt{ \frac{ 3.5 \sqrt{ 4 } }{ 10 \sqrt{ 16 } } }$$

Evaluate

$$\frac{3\sqrt{70}}{20}\approx 1.25499004$$

Solution Steps

Calculate the square root of 4 and get 2.

$$3\sqrt{\frac{3.5\times 2}{10\sqrt{16}}}$$

Multiply 3.5 and 2 to get 7.

$$3\sqrt{\frac{7}{10\sqrt{16}}}$$

Calculate the square root of 16 and get 4.

$$3\sqrt{\frac{7}{10\times 4}}$$

Multiply 10 and 4 to get 40.

$$3\sqrt{\frac{7}{40}}$$

Rewrite the square root of the division \sqrt{\frac{7}{40}} as the division of square roots \frac{\sqrt{7}}{\sqrt{40}}.

$$3\times \frac{\sqrt{7}}{\sqrt{40}}$$

Factor 40=2^{2}\times 10. Rewrite the square root of the product \sqrt{2^{2}\times 10} as the product of square roots \sqrt{2^{2}}\sqrt{10}. Take the square root of 2^{2}.

$$3\times \frac{\sqrt{7}}{2\sqrt{10}}$$

Rationalize the denominator of \frac{\sqrt{7}}{2\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$3\times \frac{\sqrt{7}\sqrt{10}}{2\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$3\times \frac{\sqrt{7}\sqrt{10}}{2\times 10}$$

To multiply \sqrt{7} and \sqrt{10}, multiply the numbers under the square root.

$$3\times \frac{\sqrt{70}}{2\times 10}$$

Multiply 2 and 10 to get 20.

$$3\times \frac{\sqrt{70}}{20}$$

Express 3\times \frac{\sqrt{70}}{20} as a single fraction.

$$\frac{3\sqrt{70}}{20}$$