Solve {left(7+6sqrt{88}right)}^2

$${ \left(7+6 \sqrt{ 88 } \right) }^{ 2 }$$

Evaluate

$$168\sqrt{22}+3217\approx 4004.98984765$$

Solution Steps

Factor 88=2^{2}\times 22. Rewrite the square root of the product \sqrt{2^{2}\times 22} as the product of square roots \sqrt{2^{2}}\sqrt{22}. Take the square root of 2^{2}.

$$\left(7+6\times 2\sqrt{22}\right)^{2}$$

Multiply 6 and 2 to get 12.

$$\left(7+12\sqrt{22}\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(7+12\sqrt{22}\right)^{2}.

$$49+168\sqrt{22}+144\left(\sqrt{22}\right)^{2}$$

The square of \sqrt{22} is 22.

$$49+168\sqrt{22}+144\times 22$$

Multiply 144 and 22 to get 3168.

$$49+168\sqrt{22}+3168$$

Add 49 and 3168 to get 3217.

$$3217+168\sqrt{22}$$

Expand

$$168 \sqrt{22} + 3217 = 4004.98984765$$

Solution Steps

Factor 88=2^{2}\times 22. Rewrite the square root of the product \sqrt{2^{2}\times 22} as the product of square roots \sqrt{2^{2}}\sqrt{22}. Take the square root of 2^{2}.

$$\left(7+6\times 2\sqrt{22}\right)^{2}$$

Multiply 6 and 2 to get 12.

$$\left(7+12\sqrt{22}\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(7+12\sqrt{22}\right)^{2}.

$$49+168\sqrt{22}+144\left(\sqrt{22}\right)^{2}$$

The square of \sqrt{22} is 22.

$$49+168\sqrt{22}+144\times 22$$

Multiply 144 and 22 to get 3168.

$$49+168\sqrt{22}+3168$$

Add 49 and 3168 to get 3217.

$$3217+168\sqrt{22}$$