Solve =3*45+3*45/sqrt{3^2+3^2sqrt{45^2+45^2}}

$$= \frac { 3 \cdot 45 + 3 \cdot 45 } { \sqrt { 3 ^ { 2 } + 3 ^ { 2 } } \sqrt { 45 ^ { 2 } + 45 ^ { 2 } } }$$

Evaluate

$$1$$

Solution Steps

Multiply 3 and 45 to get 135. Multiply 3 and 45 to get 135.

$$\frac{135+135}{\sqrt{3^{2}+3^{2}}\sqrt{45^{2}+45^{2}}}$$

Add 135 and 135 to get 270.

$$\frac{270}{\sqrt{3^{2}+3^{2}}\sqrt{45^{2}+45^{2}}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{270}{\sqrt{9+3^{2}}\sqrt{45^{2}+45^{2}}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{270}{\sqrt{9+9}\sqrt{45^{2}+45^{2}}}$$

Add 9 and 9 to get 18.

$$\frac{270}{\sqrt{18}\sqrt{45^{2}+45^{2}}}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$\frac{270}{3\sqrt{2}\sqrt{45^{2}+45^{2}}}$$

Calculate 45 to the power of 2 and get 2025.

$$\frac{270}{3\sqrt{2}\sqrt{2025+45^{2}}}$$

Calculate 45 to the power of 2 and get 2025.

$$\frac{270}{3\sqrt{2}\sqrt{2025+2025}}$$

Add 2025 and 2025 to get 4050.

$$\frac{270}{3\sqrt{2}\sqrt{4050}}$$

Factor 4050=45^{2}\times 2. Rewrite the square root of the product \sqrt{45^{2}\times 2} as the product of square roots \sqrt{45^{2}}\sqrt{2}. Take the square root of 45^{2}.

$$\frac{270}{3\sqrt{2}\times 45\sqrt{2}}$$

Multiply 3 and 45 to get 135.

$$\frac{270}{135\sqrt{2}\sqrt{2}}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\frac{270}{135\times 2}$$

Multiply 135 and 2 to get 270.

$$\frac{270}{270}$$

Divide 270 by 270 to get 1.

$$1$$

Factor

$$1$$