Solve (sqrt{968+2713}+63*86)^2

$$( \sqrt { 968 + 2713 } + 63 \times 86 ) ^ { 2 }$$

Evaluate

$$32508\sqrt{409}[phone]\approx 30015838.613512423$$

Solution Steps

Add 968 and 2713 to get 3681.

$$\left(\sqrt{3681}+63\times 86\right)^{2}$$

Factor 3681=3^{2}\times 409. Rewrite the square root of the product \sqrt{3^{2}\times 409} as the product of square roots \sqrt{3^{2}}\sqrt{409}. Take the square root of 3^{2}.

$$\left(3\sqrt{409}+63\times 86\right)^{2}$$

Multiply 63 and 86 to get 5418.

$$\left(3\sqrt{409}+5418\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3\sqrt{409}+5418\right)^{2}.

$$9\left(\sqrt{409}\right)^{2}+32508\sqrt{409}[phone]$$

The square of \sqrt{409} is 409.

$$9\times 409+32508\sqrt{409}[phone]$$

Multiply 9 and 409 to get 3681.

$$3681+32508\sqrt{409}[phone]$$

Add 3681 and 29354724 to get 29358405.

$$29358405+32508\sqrt{409}$$

Expand

$$32508 \sqrt{409} + 29358405 = 30015838.613512423$$

Solution Steps

Add 968 and 2713 to get 3681.

$$\left(\sqrt{3681}+63\times 86\right)^{2}$$

Factor 3681=3^{2}\times 409. Rewrite the square root of the product \sqrt{3^{2}\times 409} as the product of square roots \sqrt{3^{2}}\sqrt{409}. Take the square root of 3^{2}.

$$\left(3\sqrt{409}+63\times 86\right)^{2}$$

Multiply 63 and 86 to get 5418.

$$\left(3\sqrt{409}+5418\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3\sqrt{409}+5418\right)^{2}.

$$9\left(\sqrt{409}\right)^{2}+32508\sqrt{409}[phone]$$

The square of \sqrt{409} is 409.

$$9\times 409+32508\sqrt{409}[phone]$$

Multiply 9 and 409 to get 3681.

$$3681+32508\sqrt{409}[phone]$$

Add 3681 and 29354724 to get 29358405.

$$29358405+32508\sqrt{409}$$