Solve 1/2left(7*10^16+sqrt{left(7*10^16right)^2+4*{left(9.65*10^9right)}^2}right)

$$\frac{ 1 }{ 2 } \left( 7 \times { 10 }^{ 16 } + \sqrt{ { \left(7 \times { 10 }^{ 16 } \right) }^{ 2 } +4 \times { \left(9.65 \times { 10 }^{ 9 } \right) }^{ 2 } } \right)$$

Evaluate

$$50000000\left(\sqrt{490000000000037249}[phone]\right)\approx 7 \cdot 10^{16}$$

Solution Steps

Calculate 10 to the power of 16 and get 10000000000000000.

$$\frac{1}{2}\left(7\times 10000000000000000+\sqrt{\left(7\times 10^{16}\right)^{2}+4\times \left(9.65\times 10^{9}\right)^{2}}\right)$$

Multiply 7 and 10000000000000000 to get 70000000000000000.

$$\frac{1}{2}\left(70000000000000000+\sqrt{\left(7\times 10^{16}\right)^{2}+4\times \left(9.65\times 10^{9}\right)^{2}}\right)$$

Calculate 10 to the power of 16 and get 10000000000000000.

$$\frac{1}{2}\left(70000000000000000+\sqrt{\left(7\times 10000000000000000\right)^{2}+4\times \left(9.65\times 10^{9}\right)^{2}}\right)$$

Multiply 7 and 10000000000000000 to get 70000000000000000.

$$\frac{1}{2}\left(70000000000000000+\sqrt{70000000000000000^{2}+4\times \left(9.65\times 10^{9}\right)^{2}}\right)$$

Calculate 70000000000000000 to the power of 2 and get 4900000000000000000000000000000000.

$$\frac{1}{2}\left(70000000000000000+\sqrt{4900000000000000000000000000000000+4\times \left(9.65\times 10^{9}\right)^{2}}\right)$$

Calculate 10 to the power of 9 and get 1000000000.

$$\frac{1}{2}\left(70000000000000000+\sqrt{4900000000000000000000000000000000+4\times \left(9.65\times 1000000000\right)^{2}}\right)$$

Multiply 9.65 and 1000000000 to get 9650000000.

$$\frac{1}{2}\left(70000000000000000+\sqrt{4900000000000000000000000000000000+4\times 9650000000^{2}}\right)$$

Calculate 9650000000 to the power of 2 and get 93122500000000000000.

$$\frac{1}{2}\left(70000000000000000+\sqrt{4900000000000000000000000000000000+4\times 93122500000000000000}\right)$$

Multiply 4 and 93122500000000000000 to get 372490000000000000000.

$$\frac{1}{2}\left(70000000000000000+\sqrt{4900000000000000000000000000000000+372490000000000000000}\right)$$

Add 4900000000000000000000000000000000 and 372490000000000000000 to get 4900000000000372490000000000000000.

$$\frac{1}{2}\left(70000000000000000+\sqrt{4900000000000372490000000000000000}\right)$$

Factor 4900000000000372490000000000000000=100000000^{2}\times 490000000000037249. Rewrite the square root of the product \sqrt{100000000^{2}\times 490000000000037249} as the product of square roots \sqrt{100000000^{2}}\sqrt{490000000000037249}. Take the square root of 100000000^{2}.

$$\frac{1}{2}\left(70000000000000000+100000000\sqrt{490000000000037249}\right)$$

Use the distributive property to multiply \frac{1}{2} by 70000000000000000+100000000\sqrt{490000000000037249}.

$$35000000000000000+50000000\sqrt{490000000000037249}$$