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

$$\sqrt{ 121 } +2 \sqrt{ 9 } -2 \sqrt{ 25 } +(22+ \sqrt{ 16 } \div \sqrt{ 4 } ) \div (12 \times 3-2 \times \sqrt{ 36 } ) \div \sqrt{ 64 }$$

Evaluate

$$\frac{57}{8}=7.125$$

Solution Steps

Calculate the square root of 121 and get 11.

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

Calculate the square root of 9 and get 3.

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

Multiply 2 and 3 to get 6.

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

Add 11 and 6 to get 17.

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

Calculate the square root of 25 and get 5.

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

Multiply -2 and 5 to get -10.

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

Subtract 10 from 17 to get 7.

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

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.

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

Calculate the square root of 4 and get 2.

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

Add 22 and 2 to get 24.

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

Multiply 12 and 3 to get 36.

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

Calculate the square root of 36 and get 6.

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

Multiply -2 and 6 to get -12.

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

Subtract 12 from 36 to get 24.

$$7+\frac{\frac{24}{24}}{\sqrt{64}}$$

Divide 24 by 24 to get 1.

$$7+\frac{1}{\sqrt{64}}$$

Calculate the square root of 64 and get 8.

$$7+\frac{1}{8}$$

Convert 7 to fraction \frac{56}{8}.

$$\frac{56}{8}+\frac{1}{8}$$

Since \frac{56}{8} and \frac{1}{8} have the same denominator, add them by adding their numerators.

$$\frac{56+1}{8}$$

Add 56 and 1 to get 57.

$$\frac{57}{8}$$

Factor

$$\frac{3 \cdot 19}{2 ^ {3}} = 7\frac{1}{8} = 7.125$$