Solve {left(sqrt{40}+4right)}^2

$${ \left( \sqrt{ 40 } +4 \right) }^{ 2 }$$

Evaluate

$$16\sqrt{10}+56\approx 106.596442563$$

Solution Steps

Factor 40=2^{2}\times 10. Rewrite the square root of the product \sqrt{2^{2}\times 10} as the product of square roots \sqrt{2^{2}}\sqrt{10}. Take the square root of 2^{2}.

$$\left(2\sqrt{10}+4\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2\sqrt{10}+4\right)^{2}.

$$4\left(\sqrt{10}\right)^{2}+16\sqrt{10}+16$$

The square of \sqrt{10} is 10.

$$4\times 10+16\sqrt{10}+16$$

Multiply 4 and 10 to get 40.

$$40+16\sqrt{10}+16$$

Add 40 and 16 to get 56.

$$56+16\sqrt{10}$$

Expand

$$16 \sqrt{10} + 56 = 106.596442563$$

Solution Steps

Factor 40=2^{2}\times 10. Rewrite the square root of the product \sqrt{2^{2}\times 10} as the product of square roots \sqrt{2^{2}}\sqrt{10}. Take the square root of 2^{2}.

$$\left(2\sqrt{10}+4\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2\sqrt{10}+4\right)^{2}.

$$4\left(\sqrt{10}\right)^{2}+16\sqrt{10}+16$$

The square of \sqrt{10} is 10.

$$4\times 10+16\sqrt{10}+16$$

Multiply 4 and 10 to get 40.

$$40+16\sqrt{10}+16$$

Add 40 and 16 to get 56.

$$56+16\sqrt{10}$$