What is the value of
`[sqrt(1)]+[sqrt(2)]+[sqrt(3)]+…+[sqrt(49)]+[sqrt(50)]`
where [x] denoted greatest integer function?

Answer

To solve the problem, we need to evaluate the expression:

\[ [\sqrt{1}] + [\sqrt{2}] + [\sqrt{3}] + \ldots + [\sqrt{49}] + [\sqrt{50}] \]

where \([x]\) denotes the greatest integer function (also known as the floor function).

### Step-by-step Solution:

1. **Identify the values of \([\sqrt{n}]\)** for \(n = 1\) to \(50\):
- For \(n = 1\): \(\sqrt{1} = 1 \Rightarrow [\sqrt{1}] = 1\)
- For \(n = 2\): \(\sqrt{2} \approx 1.41 \Rightarrow [\sqrt{2}] = 1\)
- For \(n = 3\): \(\sqrt{3} \approx 1.73 \Rightarrow [\sqrt{3}] = 1\)
- For \(n = 4\): \(\sqrt{4} = 2 \Rightarrow [\sqrt{4}] = 2\)
- For \(n = 5\): \(\sqrt{5} \approx 2.24 \Rightarrow [\sqrt{5}] = 2\)
- For \(n = 6\): \(\sqrt{6} \approx 2.45 \Rightarrow [\sqrt{6}] = 2\)
- For \(n = 7\): \(\sqrt{7} \approx 2.65 \Rightarrow [\sqrt{7}] = 2\)
- For \(n = 8\): \(\sqrt{8} \approx 2.83 \Rightarrow [\sqrt{8}] = 2\)
- For \(n = 9\): \(\sqrt{9} = 3 \Rightarrow [\sqrt{9}] = 3\)
- For \(n = 10\): \(\sqrt{10} \approx 3.16 \Rightarrow [\sqrt{10}] = 3\)
- For \(n = 11\): \(\sqrt{11} \approx 3.32 \Rightarrow [\sqrt{11}] = 3\)
- For \(n = 12\): \(\sqrt{12} \approx 3.46 \Rightarrow [\sqrt{12}] = 3\)
- For \(n = 13\): \(\sqrt{13} \approx 3.61 \Rightarrow [\sqrt{13}] = 3\)
- For \(n = 14\): \(\sqrt{14} \approx 3.74 \Rightarrow [\sqrt{14}] = 3\)
- For \(n = 15\): \(\sqrt{15} \approx 3.87 \Rightarrow [\sqrt{15}] = 3\)
- For \(n = 16\): \(\sqrt{16} = 4 \Rightarrow [\sqrt{16}] = 4\)
- For \(n = 17\): \(\sqrt{17} \approx 4.12 \Rightarrow [\sqrt{17}] = 4\)
- For \(n = 18\): \(\sqrt{18} \approx 4.24 \Rightarrow [\sqrt{18}] = 4\)
- For \(n = 19\): \(\sqrt{19} \approx 4.36 \Rightarrow [\sqrt{19}] = 4\)
- For \(n = 20\): \(\sqrt{20} \approx 4.47 \Rightarrow [\sqrt{20}] = 4\)
- For \(n = 21\): \(\sqrt{21} \approx 4.58 \Rightarrow [\sqrt{21}] = 4\)
- For \(n = 22\): \(\sqrt{22} \approx 4.69 \Rightarrow [\sqrt{22}] = 4\)
- For \(n = 23\): \(\sqrt{23} \approx 4.79 \Rightarrow [\sqrt{23}] = 4\)
- For \(n = 24\): \(\sqrt{24} \approx 4.89 \Rightarrow [\sqrt{24}] = 4\)
- For \(n = 25\): \(\sqrt{25} = 5 \Rightarrow [\sqrt{25}] = 5\)
- For \(n = 26\): \(\sqrt{26} \approx 5.10 \Rightarrow [\sqrt{26}] = 5\)
- For \(n = 27\): \(\sqrt{27} \approx 5.19 \Rightarrow [\sqrt{27}] = 5\)
- For \(n = 28\): \(\sqrt{28} \approx 5.29 \Rightarrow [\sqrt{28}] = 5\)
- For \(n = 29\): \(\sqrt{29} \approx 5.38 \Rightarrow [\sqrt{29}] = 5\)
- For \(n = 30\): \(\sqrt{30} \approx 5.48 \Rightarrow [\sqrt{30}] = 5\)
- For \(n = 31\): \(\sqrt{31} \approx 5.57 \Rightarrow [\sqrt{31}] = 5\)
- For \(n = 32\): \(\sqrt{32} \approx 5.66 \Rightarrow [\sqrt{32}] = 5\)
- For \(n = 33\): \(\sqrt{33} \approx 5.74 \Rightarrow [\sqrt{33}] = 5\)
- For \(n = 34\): \(\sqrt{34} \approx 5.83 \Rightarrow [\sqrt{34}] = 5\)
- For \(n = 35\): \(\sqrt{35} \approx 5.92 \Rightarrow [\sqrt{35}] = 5\)
- For \(n = 36\): \(\sqrt{36} = 6 \Rightarrow [\sqrt{36}] = 6\)
- For \(n = 37\): \(\sqrt{37} \approx 6.08 \Rightarrow [\sqrt{37}] = 6\)
- For \(n = 38\): \(\sqrt{38} \approx 6.16 \Rightarrow [\sqrt{38}] = 6\)
- For \(n = 39\): \(\sqrt{39} \approx 6.24 \Rightarrow [\sqrt{39}] = 6\)
- For \(n = 40\): \(\sqrt{40} \approx 6.32 \Rightarrow [\sqrt{40}] = 6\)
- For \(n = 41\): \(\sqrt{41} \approx 6.40 \Rightarrow [\sqrt{41}] = 6\)
- For \(n = 42\): \(\sqrt{42} \approx 6.48 \Rightarrow [\sqrt{42}] = 6\)
- For \(n = 43\): \(\sqrt{43} \approx 6.56 \Rightarrow [\sqrt{43}] = 6\)
- For \(n = 44\): \(\sqrt{44} \approx 6.63 \Rightarrow [\sqrt{44}] = 6\)
- For \(n = 45\): \(\sqrt{45} \approx 6.71 \Rightarrow [\sqrt{45}] = 6\)
- For \(n = 46\): \(\sqrt{46} \approx 6.78 \Rightarrow [\sqrt{46}] = 6\)
- For \(n = 47\): \(\sqrt{47} \approx 6.86 \Rightarrow [\sqrt{47}] = 6\)
- For \(n = 48\): \(\sqrt{48} \approx 6.93 \Rightarrow [\sqrt{48}] = 6\)
- For \(n = 49\): \(\sqrt{49} = 7 \Rightarrow [\sqrt{49}] = 7\)
- For \(n = 50\): \(\sqrt{50} \approx 7.07 \Rightarrow [\sqrt{50}] = 7\)

2. **Count the contributions from each integer value**:
- From \(n = 1\) to \(3\): \([\sqrt{1}] = 1\) contributes \(3 \times 1 = 3\)
- From \(n = 4\) to \(8\): \([\sqrt{4}] = 2\) contributes \(5 \times 2 = 10\)
- From \(n = 9\) to \(15\): \([\sqrt{9}] = 3\) contributes \(7 \times 3 = 21\)
- From \(n = 16\) to \(24\): \([\sqrt{16}] = 4\) contributes \(9 \times 4 = 36\)
- From \(n = 25\) to \(34\): \([\sqrt{25}] = 5\) contributes \(10 \times 5 = 50\)
- From \(n = 35\) to \(48\): \([\sqrt{36}] = 6\) contributes \(14 \times 6 = 84\)
- From \(n = 49\) to \(50\): \([\sqrt{49}] = 7\) contributes \(2 \times 7 = 14\)

3. **Sum all contributions**:
\[ 3 + 10 + 21 + 36 + 50 + 84 + 14 = 218 \]

Thus, the final value of the expression is:

\[ \boxed{218} \]