Find the square root of 1849.

May 9, 2026Mathematics

ScanSolve AI Answer

May 9, 2026

Answer

Step 1: Pair the digits of 1849 from the right. The pairs are $18$ and $49$ .

Step 2: Find the largest integer whose square is less than or equal to the first pair, $18$ . $4^2 = 16$ , which is less than $18$ . $5^2 = 25$ , which is greater than $18$ . So, the first digit of the square root is $4$ .

\begin{array}{r} 4 \\[-3pt] \sqrt{18\,49} \\[-3pt] -16 \\[-3pt] \hline 2 \end{array}

Step 3: Bring down the next pair, $49$ , to form the new dividend, $249$ . Double the current quotient ( $4 \times 2 = 8$ ) to get the new partial divisor. Now, we need to find a digit $x$ such that $8x \times x \le 249$ . If $x=3$ , then $83 \times 3 = 249$ .

\begin{array}{r} 43 \\[-3pt] \sqrt{18\,49} \\[-3pt] -16 \downarrow \\[-3pt] \hline 249 \\[-3pt] -249 \\[-3pt] \hline 0 \end{array}

The square root of $1849$ is $43$ .

The positive square root of $1849$ is $\boxed{*43*}$ . Send me the next one 📸

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Quick Answer

Pair the digits of 1849 from the right. The pairs are 18 and 49.

Asked on May 9, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on May 9, 2026

Step 1: Pair the digits of 1849 from the right. The pairs are 18 and 49. Step 2: Find the largest integer whose square is less than or equal to the first pair, 18. 4^2 = 16, which is less than 18. 5^2 = 25, which is greater than 18. So, the first digit of the square root is 4. r 4 \\[-3pt] sqrt(18\,49) \\[-3pt] -16 \\[-3pt] 2 Step 3: Bring down the next pair, 49, to form the new dividend, 249. Double the current quotient (4 × 2 = 8) to get the new partial divisor. Now, we need to find a digit x such that 8x × x 249. If x=3, then 83 × 3 = 249. r 43 \\[-3pt] sqrt(18\,49) \\[-3pt] -16 \\[-3pt] 249 \\[-3pt] -249 \\[-3pt] 0 The square root of 1849 is 43. The positive square root of 1849 is 43. Send me the next one 📸