Solve sqrt{7^4/7^2+4^2+4^3-{2}^{3}}+sqrt{21-2*5-2}-sqrt{{left({2}^2right)}^3+{3}^2-6{2}^3}

$$\sqrt{ \frac{ { 7 }^{ 4 } }{ { 7 }^{ 2 } } + { 4 }^{ 2 } + { 4 }^{ 3 } - { 2 }^{ 3 } } + \sqrt{ 21-2 \cdot 5-2 } - \sqrt{ { \left( { 2 }^{ 2 } \right) }^{ 3 } + { 3 }^{ 2 } -6 { 2 }^{ 3 } }$$

Evaluate

$$9$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 4 to get 2.

$$\sqrt{7^{2}+4^{2}+4^{3}-2^{3}}+\sqrt{21-2\times 5-2}-\sqrt{\left(2^{2}\right)^{3}+3^{2}-6\times 2^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\sqrt{7^{2}+4^{2}+4^{3}-2^{3}}+\sqrt{21-2\times 5-2}-\sqrt{2^{6}+3^{2}-6\times 2^{3}}$$

Calculate 7 to the power of 2 and get 49.

$$\sqrt{49+4^{2}+4^{3}-2^{3}}+\sqrt{21-2\times 5-2}-\sqrt{2^{6}+3^{2}-6\times 2^{3}}$$

Calculate 4 to the power of 2 and get 16.

$$\sqrt{49+16+4^{3}-2^{3}}+\sqrt{21-2\times 5-2}-\sqrt{2^{6}+3^{2}-6\times 2^{3}}$$

Add 49 and 16 to get 65.

$$\sqrt{65+4^{3}-2^{3}}+\sqrt{21-2\times 5-2}-\sqrt{2^{6}+3^{2}-6\times 2^{3}}$$

Calculate 4 to the power of 3 and get 64.

$$\sqrt{65+64-2^{3}}+\sqrt{21-2\times 5-2}-\sqrt{2^{6}+3^{2}-6\times 2^{3}}$$

Add 65 and 64 to get 129.

$$\sqrt{129-2^{3}}+\sqrt{21-2\times 5-2}-\sqrt{2^{6}+3^{2}-6\times 2^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\sqrt{129-8}+\sqrt{21-2\times 5-2}-\sqrt{2^{6}+3^{2}-6\times 2^{3}}$$

Subtract 8 from 129 to get 121.

$$\sqrt{121}+\sqrt{21-2\times 5-2}-\sqrt{2^{6}+3^{2}-6\times 2^{3}}$$

Calculate the square root of 121 and get 11.

$$11+\sqrt{21-2\times 5-2}-\sqrt{2^{6}+3^{2}-6\times 2^{3}}$$

Multiply 2 and 5 to get 10.

$$11+\sqrt{21-10-2}-\sqrt{2^{6}+3^{2}-6\times 2^{3}}$$

Subtract 10 from 21 to get 11.

$$11+\sqrt{11-2}-\sqrt{2^{6}+3^{2}-6\times 2^{3}}$$

Subtract 2 from 11 to get 9.

$$11+\sqrt{9}-\sqrt{2^{6}+3^{2}-6\times 2^{3}}$$

Calculate the square root of 9 and get 3.

$$11+3-\sqrt{2^{6}+3^{2}-6\times 2^{3}}$$

Add 11 and 3 to get 14.

$$14-\sqrt{2^{6}+3^{2}-6\times 2^{3}}$$

Calculate 2 to the power of 6 and get 64.

$$14-\sqrt{64+3^{2}-6\times 2^{3}}$$

Calculate 3 to the power of 2 and get 9.

$$14-\sqrt{64+9-6\times 2^{3}}$$

Add 64 and 9 to get 73.

$$14-\sqrt{73-6\times 2^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$14-\sqrt{73-6\times 8}$$

Multiply 6 and 8 to get 48.

$$14-\sqrt{73-48}$$

Subtract 48 from 73 to get 25.

$$14-\sqrt{25}$$

Calculate the square root of 25 and get 5.

$$14-5$$

Subtract 5 from 14 to get 9.

$$9$$

Factor

$$3^{2}$$