Add 321−−√ + 721−−√ .
To calculate $321-\sqrt{7} + 721-\sqrt{7}$, we first simplify the individual square roots. The square root of $7$ is an irrational number, so we cannot simplify it further. So, we can write the expression as: \begin{align*}
321-\sqrt{7} + 721-\sqrt{7} &= 321 + 721 - (\sqrt{7}+\sqrt{7})\\
&= 1042 - 2\sqrt{7}\\
&= \boxed{1042-2\sqrt{7}}.
\end{align*}
To add 321−−√ and 721−−√, we first simplify each square root individually, and then add the results together.
Step 1: Simplify the square root of 321
To find the square root of 321, we need to find the largest perfect square that is less than or equal to 321. The largest perfect square less than 321 is 18^2 = 324. Since 324 is greater than 321, we know that the square root of 321 is slightly less than 18.
Step 2: Simplify the square root of 721
To find the square root of 721, we need to find the largest perfect square that is less than or equal to 721. The largest perfect square less than 721 is 26^2 = 676. Since 676 is less than 721, we know that the square root of 721 is slightly greater than 26.
Step 3: Add the simplified square roots
The simplified square root of 321 is slightly less than 18, and the simplified square root of 721 is slightly greater than 26. To add them together, we get:
Simplified square root of 321 + Simplified square root of 721 = 18 + 26 = 44
Therefore, 321−−√ + 721−−√ = 44.
To add the expressions 321−−√ and 721−−√, you first need to simplify each expression separately and then add the results together.
Let's start by simplifying the expression 321−−√:
Step 1: Take the square root of 321.
The square root of 321 is approximately 17.943.
Next, let's simplify the expression 721−−√:
Step 1: Take the square root of 721.
The square root of 721 is approximately 26.874.
Finally, add the results together:
17.943 + 26.874 ≈ 44.817.
Therefore, the sum of 321−−√ and 721−−√ is approximately 44.817.