Solve sqrt{24}+1/2sqrt{28}

$$\sqrt{ 24 } + \frac{ 1 }{ 2 } \sqrt{ 28 }$$

Evaluate

$$\sqrt{7}+2\sqrt{6}\approx 7.544730797$$

Solution Steps

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$2\sqrt{6}+\frac{1}{2}\sqrt{28}$$

Factor 28=2^{2}\times 7. Rewrite the square root of the product \sqrt{2^{2}\times 7} as the product of square roots \sqrt{2^{2}}\sqrt{7}. Take the square root of 2^{2}.

$$2\sqrt{6}+\frac{1}{2}\times 2\sqrt{7}$$

Cancel out 2 and 2.

$$2\sqrt{6}+\sqrt{7}$$

Factor

$$\sqrt{7} + 2 \sqrt{6} = 7.544730797$$