Solve sqrt{left(37*6right)^2+left(56*6right)^2}

$$\sqrt{ { \left(37 \times 6 \right) }^{ 2 } + { \left(56 \times 6 \right) }^{ 2 } }$$

Evaluate

$$6\sqrt{4505}\approx 402.715780669$$

Solution Steps

Multiply 37 and 6 to get 222.

$$\sqrt{222^{2}+\left(56\times 6\right)^{2}}$$

Calculate 222 to the power of 2 and get 49284.

$$\sqrt{49284+\left(56\times 6\right)^{2}}$$

Multiply 56 and 6 to get 336.

$$\sqrt{49284+336^{2}}$$

Calculate 336 to the power of 2 and get 112896.

$$\sqrt{49284+112896}$$

Add 49284 and 112896 to get 162180.

$$\sqrt{162180}$$

Factor 162180=6^{2}\times 4505. Rewrite the square root of the product \sqrt{6^{2}\times 4505} as the product of square roots \sqrt{6^{2}}\sqrt{4505}. Take the square root of 6^{2}.

$$6\sqrt{4505}$$