Solve (3)k^2=40(5^2-15*15)^2/20*20*20^2=

$$( 3 ) k ^ { 2 } = \frac { 40 ( 5 ^ { 2 } - 15 \times 15 ) ^ { 2 } } { 20 \times 20 \times 20 ^ { 2 } } =$$

Solve for k

$$k = \frac{\sqrt{30}}{3} \approx 1.825741858$$

$$k = -\frac{\sqrt{30}}{3} \approx -1.825741858$$

Steps by Finding Square Root

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$3k^{2}=\frac{40\left(5^{2}-15\times 15\right)^{2}}{20^{3}\times 20}$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$3k^{2}=\frac{40\left(5^{2}-15\times 15\right)^{2}}{20^{4}}$$

Calculate 5 to the power of 2 and get 25.

$$3k^{2}=\frac{40\left(25-15\times 15\right)^{2}}{20^{4}}$$

Multiply 15 and 15 to get 225.

$$3k^{2}=\frac{40\left(25-225\right)^{2}}{20^{4}}$$

Subtract 225 from 25 to get -200.

$$3k^{2}=\frac{40\left(-200\right)^{2}}{20^{4}}$$

Calculate -200 to the power of 2 and get 40000.

$$3k^{2}=\frac{40\times 40000}{20^{4}}$$

Multiply 40 and 40000 to get 1600000.

$$3k^{2}=\frac{1600000}{20^{4}}$$

Calculate 20 to the power of 4 and get 160000.

$$3k^{2}=\frac{1600000}{160000}$$

Divide 1600000 by 160000 to get 10.

$$3k^{2}=10$$

Divide both sides by 3.

$$k^{2}=\frac{10}{3}$$

Take the square root of both sides of the equation.

$$k=\frac{\sqrt{30}}{3} k=-\frac{\sqrt{30}}{3}$$

Steps Using the Quadratic Formula

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$3k^{2}=\frac{40\left(5^{2}-15\times 15\right)^{2}}{20^{3}\times 20}$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$3k^{2}=\frac{40\left(5^{2}-15\times 15\right)^{2}}{20^{4}}$$

Calculate 5 to the power of 2 and get 25.

$$3k^{2}=\frac{40\left(25-15\times 15\right)^{2}}{20^{4}}$$

Multiply 15 and 15 to get 225.

$$3k^{2}=\frac{40\left(25-225\right)^{2}}{20^{4}}$$

Subtract 225 from 25 to get -200.

$$3k^{2}=\frac{40\left(-200\right)^{2}}{20^{4}}$$

Calculate -200 to the power of 2 and get 40000.

$$3k^{2}=\frac{40\times 40000}{20^{4}}$$

Multiply 40 and 40000 to get 1600000.

$$3k^{2}=\frac{1600000}{20^{4}}$$

Calculate 20 to the power of 4 and get 160000.

$$3k^{2}=\frac{1600000}{160000}$$

Divide 1600000 by 160000 to get 10.

$$3k^{2}=10$$

Subtract 10 from both sides.

$$3k^{2}-10=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -10 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$k=\frac{0±\sqrt{0^{2}-4\times 3\left(-10\right)}}{2\times 3}$$

Square 0.

$$k=\frac{0±\sqrt{-4\times 3\left(-10\right)}}{2\times 3}$$

Multiply -4 times 3.

$$k=\frac{0±\sqrt{-12\left(-10\right)}}{2\times 3}$$

Multiply -12 times -10.

$$k=\frac{0±\sqrt{120}}{2\times 3}$$

Take the square root of 120.

$$k=\frac{0±2\sqrt{30}}{2\times 3}$$

Multiply 2 times 3.

$$k=\frac{0±2\sqrt{30}}{6}$$

Now solve the equation k=\frac{0±2\sqrt{30}}{6} when ± is plus.

$$k=\frac{\sqrt{30}}{3}$$

Now solve the equation k=\frac{0±2\sqrt{30}}{6} when ± is minus.

$$k=-\frac{\sqrt{30}}{3}$$

The equation is now solved.

$$k=\frac{\sqrt{30}}{3} k=-\frac{\sqrt{30}}{3}$$