Solve frac{sqrt{3}sqrt{12}}{sqrt{0,16}+sqrt{0,36}}

$$\frac { \sqrt { 3 } \sqrt { 12 } } { \sqrt { 0,16 } + \sqrt { 0,36 } }$$

Evaluate

$$6$$

Solution Steps

Factor 12=3\times 4. Rewrite the square root of the product \sqrt{3\times 4} as the product of square roots \sqrt{3}\sqrt{4}.

$$\frac{\sqrt{3}\sqrt{3}\sqrt{4}}{\sqrt{0,16}+\sqrt{0,36}}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{3\sqrt{4}}{\sqrt{0,16}+\sqrt{0,36}}$$

Calculate the square root of 4 and get 2.

$$\frac{3\times 2}{\sqrt{0,16}+\sqrt{0,36}}$$

Multiply 3 and 2 to get 6.

$$\frac{6}{\sqrt{0,16}+\sqrt{0,36}}$$

Calculate the square root of 0,16 and get 0,4.

$$\frac{6}{0,4+\sqrt{0,36}}$$

Calculate the square root of 0,36 and get 0,6.

$$\frac{6}{0,4+0,6}$$

Add 0,4 and 0,6 to get 1.

$$\frac{6}{1}$$

Anything divided by one gives itself.

$$6$$

Factor

$$2\times 3$$