Solve sqrt{1/1-frac{400^2{9*10^16}}}

$$\sqrt { \frac { 1 } { 1 - \frac { 400 ^ { 2 } } { 9 \cdot 10 ^ { 16 } } } }$$

Evaluate

$$\frac{750000\sqrt{562499999999}}{562499999999}\approx 1$$

Solution Steps

Calculate 400 to the power of 2 and get 160000.

$$\sqrt{\frac{1}{1-\frac{160000}{9\times 10^{16}}}}$$

Calculate 10 to the power of 16 and get 10000000000000000.

$$\sqrt{\frac{1}{1-\frac{160000}{9\times 10000000000000000}}}$$

Multiply 9 and 10000000000000000 to get 90000000000000000.

$$\sqrt{\frac{1}{1-\frac{160000}{90000000000000000}}}$$

Reduce the fraction \frac{160000}{90000000000000000} to lowest terms by extracting and canceling out 160000.

$$\sqrt{\frac{1}{1-\frac{1}{562500000000}}}$$

Convert 1 to fraction \frac{562500000000}{562500000000}.

$$\sqrt{\frac{1}{\frac{562500000000}{562500000000}-\frac{1}{562500000000}}}$$

Since \frac{562500000000}{562500000000} and \frac{1}{562500000000} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{1}{\frac{562500000000-1}{562500000000}}}$$

Subtract 1 from 562500000000 to get 562499999999.

$$\sqrt{\frac{1}{\frac{562499999999}{562500000000}}}$$

Divide 1 by \frac{562499999999}{562500000000} by multiplying 1 by the reciprocal of \frac{562499999999}{562500000000}.

$$\sqrt{1\times \frac{562500000000}{562499999999}}$$

Multiply 1 and \frac{562500000000}{562499999999} to get \frac{562500000000}{562499999999}.

$$\sqrt{\frac{562500000000}{562499999999}}$$

Rewrite the square root of the division \sqrt{\frac{562500000000}{562499999999}} as the division of square roots \frac{\sqrt{562500000000}}{\sqrt{562499999999}}.

$$\frac{\sqrt{562500000000}}{\sqrt{562499999999}}$$

Calculate the square root of 562500000000 and get 750000.

$$\frac{750000}{\sqrt{562499999999}}$$

Rationalize the denominator of \frac{750000}{\sqrt{562499999999}} by multiplying numerator and denominator by \sqrt{562499999999}.

$$\frac{750000\sqrt{562499999999}}{\left(\sqrt{562499999999}\right)^{2}}$$

The square of \sqrt{562499999999} is 562499999999.

$$\frac{750000\sqrt{562499999999}}{562499999999}$$