Solve sqrt{3}sqrt{12}+frac{sqrt{56}}{sqrt{14}}

$$\sqrt{ 3 } \sqrt{ 12 } + \frac{ \sqrt{ 56 } }{ \sqrt{ 14 } }$$

Evaluate

$$8$$

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}.

$$\sqrt{3}\sqrt{3}\sqrt{4}+\frac{\sqrt{56}}{\sqrt{14}}$$

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

$$3\sqrt{4}+\frac{\sqrt{56}}{\sqrt{14}}$$

Calculate the square root of 4 and get 2.

$$3\times 2+\frac{\sqrt{56}}{\sqrt{14}}$$

Multiply 3 and 2 to get 6.

$$6+\frac{\sqrt{56}}{\sqrt{14}}$$

Rewrite the division of square roots \frac{\sqrt{56}}{\sqrt{14}} as the square root of the division \sqrt{\frac{56}{14}} and perform the division.

$$6+\sqrt{4}$$

Calculate the square root of 4 and get 2.

$$6+2$$

Add 6 and 2 to get 8.

$$8$$

Factor

$$2^{3}$$