Solve sqrt{121}+2sqrt{9}-2sqrt{25}+frac{22+frac{sqrt{16}}{sqrt{4}}}{12*3-2sqrt{36}divsqrt{64}}

$$\sqrt{ 121 } +2 \sqrt{ 9 } -2 \sqrt{ 25 } + \frac{ 22+ \frac{ \sqrt{ 16 } }{ \sqrt{ 4 } } }{ 12 \cdot 3-2 \sqrt{ 36 } \div \sqrt{ 64 } }$$

Evaluate

$$\frac{177}{23}\approx 7.695652174$$

Solution Steps

Calculate the square root of 121 and get 11.

$$11+2\sqrt{9}-2\sqrt{25}+\frac{22+\frac{\sqrt{16}}{\sqrt{4}}}{12\times 3-\frac{2\sqrt{36}}{\sqrt{64}}}$$

Calculate the square root of 9 and get 3.

$$11+2\times 3-2\sqrt{25}+\frac{22+\frac{\sqrt{16}}{\sqrt{4}}}{12\times 3-\frac{2\sqrt{36}}{\sqrt{64}}}$$

Multiply 2 and 3 to get 6.

$$11+6-2\sqrt{25}+\frac{22+\frac{\sqrt{16}}{\sqrt{4}}}{12\times 3-\frac{2\sqrt{36}}{\sqrt{64}}}$$

Add 11 and 6 to get 17.

$$17-2\sqrt{25}+\frac{22+\frac{\sqrt{16}}{\sqrt{4}}}{12\times 3-\frac{2\sqrt{36}}{\sqrt{64}}}$$

Calculate the square root of 25 and get 5.

$$17-2\times 5+\frac{22+\frac{\sqrt{16}}{\sqrt{4}}}{12\times 3-\frac{2\sqrt{36}}{\sqrt{64}}}$$

Multiply -2 and 5 to get -10.

$$17-10+\frac{22+\frac{\sqrt{16}}{\sqrt{4}}}{12\times 3-\frac{2\sqrt{36}}{\sqrt{64}}}$$

Subtract 10 from 17 to get 7.

$$7+\frac{22+\frac{\sqrt{16}}{\sqrt{4}}}{12\times 3-\frac{2\sqrt{36}}{\sqrt{64}}}$$

Rewrite the division of square roots \frac{\sqrt{16}}{\sqrt{4}} as the square root of the division \sqrt{\frac{16}{4}} and perform the division.

$$7+\frac{22+\sqrt{4}}{12\times 3-\frac{2\sqrt{36}}{\sqrt{64}}}$$

Calculate the square root of 4 and get 2.

$$7+\frac{22+2}{12\times 3-\frac{2\sqrt{36}}{\sqrt{64}}}$$

Add 22 and 2 to get 24.

$$7+\frac{24}{12\times 3-\frac{2\sqrt{36}}{\sqrt{64}}}$$

Multiply 12 and 3 to get 36.

$$7+\frac{24}{36-\frac{2\sqrt{36}}{\sqrt{64}}}$$

Calculate the square root of 36 and get 6.

$$7+\frac{24}{36-\frac{2\times 6}{\sqrt{64}}}$$

Multiply 2 and 6 to get 12.

$$7+\frac{24}{36-\frac{12}{\sqrt{64}}}$$

Calculate the square root of 64 and get 8.

$$7+\frac{24}{36-\frac{12}{8}}$$

Reduce the fraction \frac{12}{8} to lowest terms by extracting and canceling out 4.

$$7+\frac{24}{36-\frac{3}{2}}$$

Convert 36 to fraction \frac{72}{2}.

$$7+\frac{24}{\frac{72}{2}-\frac{3}{2}}$$

Since \frac{72}{2} and \frac{3}{2} have the same denominator, subtract them by subtracting their numerators.

$$7+\frac{24}{\frac{72-3}{2}}$$

Subtract 3 from 72 to get 69.

$$7+\frac{24}{\frac{69}{2}}$$

Divide 24 by \frac{69}{2} by multiplying 24 by the reciprocal of \frac{69}{2}.

$$7+24\times \frac{2}{69}$$

Express 24\times \frac{2}{69} as a single fraction.

$$7+\frac{24\times 2}{69}$$

Multiply 24 and 2 to get 48.

$$7+\frac{48}{69}$$

Reduce the fraction \frac{48}{69} to lowest terms by extracting and canceling out 3.

$$7+\frac{16}{23}$$

Convert 7 to fraction \frac{161}{23}.

$$\frac{161}{23}+\frac{16}{23}$$

Since \frac{161}{23} and \frac{16}{23} have the same denominator, add them by adding their numerators.

$$\frac{161+16}{23}$$

Add 161 and 16 to get 177.

$$\frac{177}{23}$$

Factor

$$\frac{3 \cdot 59}{23} = 7\frac{16}{23} = 7.695652173913044$$