Solve (3^2divsqrt{81})+(sqrt{625}div5^2)div(sqrt{16}div2^2)

$$( { 3 }^{ 2 } \div \sqrt{ 81 } )+( \sqrt{ 625 } \div { 5 }^{ 2 } ) \div ( \sqrt{ 16 } \div { 2 }^{ 2 } )$$

Evaluate

$$2$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$\frac{9}{\sqrt{81}}+\frac{\frac{\sqrt{625}}{5^{2}}}{\frac{\sqrt{16}}{2^{2}}}$$

Calculate the square root of 81 and get 9.

$$\frac{9}{9}+\frac{\frac{\sqrt{625}}{5^{2}}}{\frac{\sqrt{16}}{2^{2}}}$$

Divide 9 by 9 to get 1.

$$1+\frac{\frac{\sqrt{625}}{5^{2}}}{\frac{\sqrt{16}}{2^{2}}}$$

Divide \frac{\sqrt{625}}{5^{2}} by \frac{\sqrt{16}}{2^{2}} by multiplying \frac{\sqrt{625}}{5^{2}} by the reciprocal of \frac{\sqrt{16}}{2^{2}}.

$$1+\frac{\sqrt{625}\times 2^{2}}{5^{2}\sqrt{16}}$$

Calculate the square root of 625 and get 25.

$$1+\frac{25\times 2^{2}}{5^{2}\sqrt{16}}$$

Calculate 2 to the power of 2 and get 4.

$$1+\frac{25\times 4}{5^{2}\sqrt{16}}$$

Multiply 25 and 4 to get 100.

$$1+\frac{100}{5^{2}\sqrt{16}}$$

Calculate 5 to the power of 2 and get 25.

$$1+\frac{100}{25\sqrt{16}}$$

Calculate the square root of 16 and get 4.

$$1+\frac{100}{25\times 4}$$

Multiply 25 and 4 to get 100.

$$1+\frac{100}{100}$$

Divide 100 by 100 to get 1.

$$1+1$$

Add 1 and 1 to get 2.

$$2$$

Factor

$$2$$