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2 <p>Last updated on<strong>August 5, 2025</strong></p>

3 <p>A square root is a number that, when we double it, it gives you another number. It is a very important and interesting part of mathematics. You must have applied it for measuring each side of a square from the total area.</p>

4 <h2>What is the Square Root of 250?</h2>

5 <p>The<a>square</a>root<a>of</a>250 is a<a>number</a>, when we multiply it by itself we get 250. The square root of 250 is an<a>irrational number</a>. As it cannot be written as a<a>ratio</a>of two numbers. It is denoted by 250 and is approximately equal to 15.8114. </p>

6 <p>Exponential form : 2501/2 ≅ 15.8114.</p>

7 <p>Radical Form: √250 </p>

8 <h2>Finding the Square Root of 250</h2>

9 <p>We can find the<a>square root</a>of a number by using methods like: Prime Factorization; Long Division method; Approximation method and Subtraction method: </p>

10 <h3>Prime Factorization</h3>

11 <p>The factoring of a number into smaller numbers is<a>prime factorization</a>. Here, 250 is a<a>composite number</a>, it can be broken down into smaller numbers more than 2.</p>

12 <p>250 = 2×5×5×5 = 2×53</p>

13 <p>Taking out the<a>perfect square</a>,</p>

14 <p>√250 = √25x10 = 5√10</p>

15 <p> So, from this method we cannot find the exact square root, but we confirm that 250 is not a perfect square.</p>

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18 <h3>Long Division Method</h3>

17 <h3>Long Division Method</h3>

19 <p>In this method, we get to find the value of the square root precisely.</p>

18 <p>In this method, we get to find the value of the square root precisely.</p>

20 <p>Grouping the digits: We start with pairing the digits from the<a>decimal</a>part 250.00</p>

19 <p>Grouping the digits: We start with pairing the digits from the<a>decimal</a>part 250.00</p>

21 <p>Find the number whose square will be<a>less than</a>or equal to 250<a>i</a>.e., 152=225</p>

20 <p>Find the number whose square will be<a>less than</a>or equal to 250<a>i</a>.e., 152=225</p>

22 <p>Subtract 152=225 from 250, which leaves us with 25.</p>

21 <p>Subtract 152=225 from 250, which leaves us with 25.</p>

23 <p>Now we bring down two zeros, which makes it 2500</p>

22 <p>Now we bring down two zeros, which makes it 2500</p>

24 <p>Next double the<a>divisor</a>15, we get 30. Next we find the largest digit which will be lesser than or equal to 2500.</p>

23 <p>Next double the<a>divisor</a>15, we get 30. Next we find the largest digit which will be lesser than or equal to 2500.</p>

25 <p>Repeat the steps to get the next decimal places.</p>

24 <p>Repeat the steps to get the next decimal places.</p>

26 <p>So after calculation we get, √250 = 15.8114</p>

25 <p>So after calculation we get, √250 = 15.8114</p>

27 <h3>Approximation Method</h3>

26 <h3>Approximation Method</h3>

28 <p>As 152 =225 and 162 =256, the square root of 250 lies between 15 and 16.</p>

27 <p>As 152 =225 and 162 =256, the square root of 250 lies between 15 and 16.</p>

29 <p>Start by guessing 15.62 which is nearest to 15.</p>

28 <p>Start by guessing 15.62 which is nearest to 15.</p>

30 <p>15.82 = 249.64 which too less</p>

29 <p>15.82 = 249.64 which too less</p>

31 <p>Go to the next number 15.7, 15.822 = 250.27 which is too high.</p>

30 <p>Go to the next number 15.7, 15.822 = 250.27 which is too high.</p>

32 <p>So, 250 = 15.811 </p>

31 <p>So, 250 = 15.811 </p>

33 <h3>Subtraction Method</h3>

32 <h3>Subtraction Method</h3>

34 <p> The<a>subtraction</a>method includes subtracting consecutive<a>odd numbers</a>from 250 to see how many steps we need to reach zero. However, since 250 is not a perfect square, we cannot exactly reach 0. </p>

33 <p> The<a>subtraction</a>method includes subtracting consecutive<a>odd numbers</a>from 250 to see how many steps we need to reach zero. However, since 250 is not a perfect square, we cannot exactly reach 0. </p>

35 <p>250 -1 =249</p>

34 <p>250 -1 =249</p>

36 <p>249-3=246</p>

35 <p>249-3=246</p>

37 <p>246-5=241</p>

36 <p>246-5=241</p>

38 <p>As we did not get zero, we understand that 250 is not a perfect square. </p>

37 <p>As we did not get zero, we understand that 250 is not a perfect square. </p>

39 <h2>Common Mistakes and How to Avoid Them in the Square Root of 250</h2>

38 <h2>Common Mistakes and How to Avoid Them in the Square Root of 250</h2>

40 <p>While learning about Square root, students are likely to make mistakes. Below-mentioned are a few mistakes with solutions on how to avoid them: </p>

39 <p>While learning about Square root, students are likely to make mistakes. Below-mentioned are a few mistakes with solutions on how to avoid them: </p>

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41 <h3>Problem 1</h3>

42 <p>If, x²=250, find the value of x.</p>

43 <p>Okay, lets begin</p>

44 <p>If, x2=250</p>

45 <p>Then, </p>

46 <p>x= 250 </p>

47 <h3>Explanation</h3>

48 <p> Here is the square when shifted to the RHS it becomes the square root of the number</p>

49 <p>x= 577 </p>

50 <p>x=75</p>

51 <p>So the value of x is 75.</p>

52 <p>Well explained 👍</p>

53 <h3>Problem 2</h3>

54 <p>Verify if √250 is greater than 15.</p>

55 <p>Okay, lets begin</p>

56 <p>First, approximate √250 :</p>

57 <p>Using prime factorization:</p>

58 <p>√250 = √5x49 = 7√5</p>

59 <p>Since √5 = 2.236</p>

60 <p>7√5 = 7 × 2.236 =15.652</p>

61 <p>Since 15.652>15, we conclude that : </p>

62 <p>√250 > 15</p>

63 <h3>Explanation</h3>

64 <p>The approximation of √250 shows us that it is greater than 15.</p>

65 <p>Well explained 👍</p>

66 <h3>Problem 3</h3>

67 <p>Express the square root of 250 in the simplest radical form.</p>

68 <p>Okay, lets begin</p>

69 <p>√250 = 5 × 72</p>

70 <p>We use the square root property:</p>

71 <p>√250 =√5x7x7 </p>

72 <p>Now take out the square of the number which is 7×7 = 49, take out 7.</p>

73 <p>√250 = 7√5 </p>

74 <p>So, the value is 7√5 .</p>

75 <h3>Explanation</h3>

76 <p>Square root in terms of radical form is 7√5</p>

77 <p>Well explained 👍</p>

78 <h3>Problem 4</h3>

79 <p>Solve: 20/√250</p>

80 <p>Okay, lets begin</p>

81 <p> To simplify, 20/ √250 , we multiply the number in the denominator with the numerator and the denominator, which is called rationalizing. </p>

82 <h3>Explanation</h3>

83 <p>20/√250 x √250 / √250 = 20√250 /√250 , here when two square roots with the same number are multiplied the roots get canceled (in the denominator), and we are left with the same number, hence√ 250 x √250 = 250.</p>

84 <p>After rationalizing, we get, 20 √250 / 250 </p>

85 <p>Well explained 👍</p>

86 <h3>Problem 5</h3>

87 <p>Simplify √25+√250</p>

88 <p>Okay, lets begin</p>

89 <p>√25+√250 here we have a root inside a root, which is called a nested root. </p>

90 <p>Explanation: We first find the square root of the number that is inside, √250 =15.811</p>

91 <p>=√ 25+15.811 </p>

92 <p>Now we add both the numbers. We get,</p>

93 <p>= √40.811 , next we find the square root of 40.811</p>

94 <p>= 6.39</p>

95 <h3>Explanation</h3>

96 <p>Answer: = 6.39 </p>

97 <p>Well explained 👍</p>

98 <h2>FAQs on 250 Square Root</h2>

99 <h3>1.Is 250 a perfect square root?</h3>

100 <p>250 is not a perfect square number, as we cannot find any number that can be multiplied to get 250. </p>

101 <h3>2.What are the factors of 250?</h3>

102 <p>The<a>factors</a>of 250 are 1,2,5,10,25,50,125 and 250. It is a composite number. </p>

103 <h3>3.What is the value of √250 the nearest whole number?</h3>

104 <h3>4.What perfect Squares go into 250?</h3>

105 <p>Solution: 25×5×2=250</p>

106 <p>The greatest perfect square which is the factor of 250 and is required is 25. </p>

107 <h3>5.What is 250 a perfect cube?</h3>

108 <p>In a triplet, the prime factor 2 will not appear. Hence, 250 is not a<a>perfect cube</a>. </p>

109 <h2>Important Glossaries for Square Root of 250</h2>

110 <ul><li><strong>Irrational number:</strong>A number that cannot be written in the form of a ratio or fraction. For example, √250 is an irrational number.</li>

111 </ul><ul><li><strong>Exponent form:</strong>Writing the square root of a number in the form of degree or powers. For example, 2501/2 ≅ 4.7958</li>

112 </ul><ul><li><strong>Square root:</strong>It is a number that, when we double it, it gives you another number. For example, 4 × 4 =16. </li>

113 </ul><p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>

114 <p>▶</p>

115 <h2>Jaskaran Singh Saluja</h2>

116 <h3>About the Author</h3>

117 <p>Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.</p>

118 <h3>Fun Fact</h3>

119 <p>: He loves to play the quiz with kids through algebra to make kids love it.</p>