Video: Simplifying Numerical Expressions Involving Square Roots

Express (10 + √17)² + 75 in its simplest form.

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Video Transcript

Express 10 plus square root 17 all squared plus 75 in its simplest form.

To begin, we will rewrite the parenthesis that is squared by writing it twice, multiplying it to itself, and then bringing down the 75. So now we need to FOIL or distribute through the parentheses. So we have F is what we begin with with FOILing.

The first terms in the parenthesis we multiply together. So 10 times 10 is 100. Then we multiply the outside numbers together, 10 times the square root of 17. However, 10 is outside of a square root and 17 is inside of a square root. So we leave it as 10 square root 17.

Next, we multiply the inside numbers together, so square root 17 times 10, which we will write the 10 first and then the square root 17 next to it. And lastly, we multiply the last numbers together, square root 17 times square root 17, which is equal to 17. And now we bring down our 75.

So our next step would be to combine like terms. We have 100, 17, and 75 to add together, which is equal to 192. And then 10 square root 17 plus 10 square root 17 is equal to 20 square root 17, because we add the numbers outside the parentheses together. And then the number inside the square root has to be the same. It almost works as a variable when adding. Therefore, our final answer in its simplest form would be 192 plus 20 square root 17.

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