Solve sqrt{4*4+4*4+2*2+6*6+4*4/5+1}

$$\sqrt{ \frac{ 4 \cdot 4+4 \cdot 4+2 \cdot 2+6 \cdot 6+4 \cdot 4 }{ 5+1 } }$$

Evaluate

$$\frac{2\sqrt{33}}{3}\approx 3.829708431$$

Solution Steps

Multiply 4 and 4 to get 16. Multiply 4 and 4 to get 16. Multiply 2 and 2 to get 4. Multiply 6 and 6 to get 36. Multiply 4 and 4 to get 16.

$$\sqrt{\frac{16+16+4+36+16}{5+1}}$$

Add 16 and 16 to get 32.

$$\sqrt{\frac{32+4+36+16}{5+1}}$$

Add 32 and 4 to get 36.

$$\sqrt{\frac{36+36+16}{5+1}}$$

Add 36 and 36 to get 72.

$$\sqrt{\frac{72+16}{5+1}}$$

Add 72 and 16 to get 88.

$$\sqrt{\frac{88}{5+1}}$$

Add 5 and 1 to get 6.

$$\sqrt{\frac{88}{6}}$$

Reduce the fraction \frac{88}{6} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{44}{3}}$$

Rewrite the square root of the division \sqrt{\frac{44}{3}} as the division of square roots \frac{\sqrt{44}}{\sqrt{3}}.

$$\frac{\sqrt{44}}{\sqrt{3}}$$

Factor 44=2^{2}\times 11. Rewrite the square root of the product \sqrt{2^{2}\times 11} as the product of square roots \sqrt{2^{2}}\sqrt{11}. Take the square root of 2^{2}.

$$\frac{2\sqrt{11}}{\sqrt{3}}$$

Rationalize the denominator of \frac{2\sqrt{11}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{2\sqrt{11}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{2\sqrt{11}\sqrt{3}}{3}$$

To multiply \sqrt{11} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{2\sqrt{33}}{3}$$