Solve 79/16+sqrt{46*76}4+437^+246^2

$$\frac{ 79 }{ 16 } + \sqrt{ 46 \times 76 } 4+ { 437 }^{ +2 } { 46 }^{ 2 }$$

Evaluate

$$8\sqrt{874}+\frac{6465446543}{16}\approx 404090645.445428014$$

Solution Steps

Multiply 46 and 76 to get 3496.

$$\frac{79}{16}+4\sqrt{3496}+437^{2}\times 46^{2}$$

Factor 3496=2^{2}\times 874. Rewrite the square root of the product \sqrt{2^{2}\times 874} as the product of square roots \sqrt{2^{2}}\sqrt{874}. Take the square root of 2^{2}.

$$\frac{79}{16}+4\times 2\sqrt{874}+437^{2}\times 46^{2}$$

Multiply 4 and 2 to get 8.

$$\frac{79}{16}+8\sqrt{874}+437^{2}\times 46^{2}$$

Calculate 437 to the power of 2 and get 190969.

$$\frac{79}{16}+8\sqrt{874}+190969\times 46^{2}$$

Calculate 46 to the power of 2 and get 2116.

$$\frac{79}{16}+8\sqrt{874}+190969\times 2116$$

Multiply 190969 and 2116 to get 404090404.

$$\frac{79}{16}+8\sqrt{874}[phone]$$

Convert 404090404 to fraction \frac{6465446464}{16}.

$$\frac{79}{16}+8\sqrt{874}+\frac{6465446464}{16}$$

Since \frac{79}{16} and \frac{6465446464}{16} have the same denominator, add them by adding their numerators.

$$\frac{79+6465446464}{16}+8\sqrt{874}$$

Add 79 and 6465446464 to get 6465446543.

$$\frac{6465446543}{16}+8\sqrt{874}$$

Factor

$$\frac{128 \sqrt{874} + 6465446543}{16} = 404090645.445428$$