Solve (5sqrt{6}-sqrt{5})^2

$$( 5 \sqrt { 6 } - \sqrt { 5 } ) ^ { 2 }$$

Evaluate

$$155-10\sqrt{30}\approx 100.227744249$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(5\sqrt{6}-\sqrt{5}\right)^{2}.

$$25\left(\sqrt{6}\right)^{2}-10\sqrt{6}\sqrt{5}+\left(\sqrt{5}\right)^{2}$$

The square of \sqrt{6} is 6.

$$25\times 6-10\sqrt{6}\sqrt{5}+\left(\sqrt{5}\right)^{2}$$

Multiply 25 and 6 to get 150.

$$150-10\sqrt{6}\sqrt{5}+\left(\sqrt{5}\right)^{2}$$

To multiply \sqrt{6} and \sqrt{5}, multiply the numbers under the square root.

$$150-10\sqrt{30}+\left(\sqrt{5}\right)^{2}$$

The square of \sqrt{5} is 5.

$$150-10\sqrt{30}+5$$

Add 150 and 5 to get 155.

$$155-10\sqrt{30}$$

Expand

$$155-10\sqrt{30}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(5\sqrt{6}-\sqrt{5}\right)^{2}.

$$25\left(\sqrt{6}\right)^{2}-10\sqrt{6}\sqrt{5}+\left(\sqrt{5}\right)^{2}$$

The square of \sqrt{6} is 6.

$$25\times 6-10\sqrt{6}\sqrt{5}+\left(\sqrt{5}\right)^{2}$$

Multiply 25 and 6 to get 150.

$$150-10\sqrt{6}\sqrt{5}+\left(\sqrt{5}\right)^{2}$$

To multiply \sqrt{6} and \sqrt{5}, multiply the numbers under the square root.

$$150-10\sqrt{30}+\left(\sqrt{5}\right)^{2}$$

The square of \sqrt{5} is 5.

$$150-10\sqrt{30}+5$$

Add 150 and 5 to get 155.

$$155-10\sqrt{30}$$