Solve k^2=100(41*18-9*32)^2/9*41*18*32=

$$k ^ { 2 } = \frac { 100 ( 41 \times 18 - 9 \times 32 ) ^ { 2 } } { 9 \times 41 \times 18 \times 32 } =$$

Solve for k

$$k = \frac{125 \sqrt{41}}{82} \approx 9.760860118$$

$$k = -\frac{125 \sqrt{41}}{82} \approx -9.760860118$$

Steps by Finding Square Root

Cancel out 2\times 2 in both numerator and denominator.

$$k^{2}=\frac{25\left(18\times 41-9\times 32\right)^{2}}{9\times 9\times 16\times 41}$$

Multiply 18 and 41 to get 738.

$$k^{2}=\frac{25\left(738-9\times 32\right)^{2}}{9\times 9\times 16\times 41}$$

Multiply 9 and 32 to get 288.

$$k^{2}=\frac{25\left(738-288\right)^{2}}{9\times 9\times 16\times 41}$$

Subtract 288 from 738 to get 450.

$$k^{2}=\frac{25\times 450^{2}}{9\times 9\times 16\times 41}$$

Calculate 450 to the power of 2 and get 202500.

$$k^{2}=\frac{25\times 202500}{9\times 9\times 16\times 41}$$

Multiply 25 and 202500 to get 5062500.

$$k^{2}=\frac{5062500}{9\times 9\times 16\times 41}$$

Multiply 9 and 9 to get 81.

$$k^{2}=\frac{5062500}{81\times 16\times 41}$$

Multiply 81 and 16 to get 1296.

$$k^{2}=\frac{5062500}{1296\times 41}$$

Multiply 1296 and 41 to get 53136.

$$k^{2}=\frac{5062500}{53136}$$

Reduce the fraction \frac{5062500}{53136} to lowest terms by extracting and canceling out 324.

$$k^{2}=\frac{15625}{164}$$

Take the square root of both sides of the equation.

$$k=\frac{125\sqrt{41}}{82} k=-\frac{125\sqrt{41}}{82}$$

Steps Using the Quadratic Formula

Cancel out 2\times 2 in both numerator and denominator.

$$k^{2}=\frac{25\left(18\times 41-9\times 32\right)^{2}}{9\times 9\times 16\times 41}$$

Multiply 18 and 41 to get 738.

$$k^{2}=\frac{25\left(738-9\times 32\right)^{2}}{9\times 9\times 16\times 41}$$

Multiply 9 and 32 to get 288.

$$k^{2}=\frac{25\left(738-288\right)^{2}}{9\times 9\times 16\times 41}$$

Subtract 288 from 738 to get 450.

$$k^{2}=\frac{25\times 450^{2}}{9\times 9\times 16\times 41}$$

Calculate 450 to the power of 2 and get 202500.

$$k^{2}=\frac{25\times 202500}{9\times 9\times 16\times 41}$$

Multiply 25 and 202500 to get 5062500.

$$k^{2}=\frac{5062500}{9\times 9\times 16\times 41}$$

Multiply 9 and 9 to get 81.

$$k^{2}=\frac{5062500}{81\times 16\times 41}$$

Multiply 81 and 16 to get 1296.

$$k^{2}=\frac{5062500}{1296\times 41}$$

Multiply 1296 and 41 to get 53136.

$$k^{2}=\frac{5062500}{53136}$$

Reduce the fraction \frac{5062500}{53136} to lowest terms by extracting and canceling out 324.

$$k^{2}=\frac{15625}{164}$$

Subtract \frac{15625}{164} from both sides.

$$k^{2}-\frac{15625}{164}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{15625}{164} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$k=\frac{0±\sqrt{0^{2}-4\left(-\frac{15625}{164}\right)}}{2}$$

Square 0.

$$k=\frac{0±\sqrt{-4\left(-\frac{15625}{164}\right)}}{2}$$

Multiply -4 times -\frac{15625}{164}.

$$k=\frac{0±\sqrt{\frac{15625}{41}}}{2}$$

Take the square root of \frac{15625}{41}.

$$k=\frac{0±\frac{125\sqrt{41}}{41}}{2}$$

Now solve the equation k=\frac{0±\frac{125\sqrt{41}}{41}}{2} when ± is plus.

$$k=\frac{125\sqrt{41}}{82}$$

Now solve the equation k=\frac{0±\frac{125\sqrt{41}}{41}}{2} when ± is minus.

$$k=-\frac{125\sqrt{41}}{82}$$

The equation is now solved.

$$k=\frac{125\sqrt{41}}{82} k=-\frac{125\sqrt{41}}{82}$$