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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 245?</h2>

5 <p>The<a>square</a>root<a>of</a>245 is a<a>number</a>, when we multiply it by itself we get 245. The square root of 245 is an<a>irrational number</a>. As it cannot be written as a<a>ratio</a>of two numbers. It is denoted by 245 and is approximately equal to 15.6525. </p>

6 <p>Exponential form : 2451/2 ≅ 15.6525. Radical Form: √245 </p>

7 <h2>Finding the Square Root of 245</h2>

8 <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>

9 <h2>Prime Factorization</h2>

10 <p>The factoring of a number into smaller numbers is<a>prime factorization</a>. Here, 245 is a<a>composite number</a>, it can be broken down into smaller numbers more than 2.</p>

11 <p>√245 = √5×7×7 = 5x72</p>

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

13 <p>√245 =√ 5x7x7 = 7√5 =15.6525</p>

14 <p> So, from this method we cannot find the exact square root, but we confirm that 245 is not a perfect square</p>

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17 <h3>Long Division Method</h3>

16 <h3>Long Division Method</h3>

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

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

19 <p>Grouping the digits: We start with pairing the digits from the<a>decimal</a>part 245.00</p>

18 <p>Grouping the digits: We start with pairing the digits from the<a>decimal</a>part 245.00</p>

20 <p>Find the number whose square will be<a>less than</a>or equal to 245<a>i</a>.e., 152=225</p>

19 <p>Find the number whose square will be<a>less than</a>or equal to 245<a>i</a>.e., 152=225</p>

21 <p>Subtract 152=225 from 245, which leaves us with 20.</p>

20 <p>Subtract 152=225 from 245, which leaves us with 20.</p>

22 <p>Now we bring down two zeros, which makes it 2000</p>

21 <p>Now we bring down two zeros, which makes it 2000</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 2000.</p>

22 <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 2000.</p>

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

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

25 <p>So after calculation we get, √245 = 15.6525</p>

24 <p>So after calculation we get, √245 = 15.6525</p>

26 <h3>Approximation Method</h3>

25 <h3>Approximation Method</h3>

27 <p>As 152 =225 and 162 =256, the square root of 245 lies between 15 and 16.</p>

26 <p>As 152 =225 and 162 =256, the square root of 245 lies between 15 and 16.</p>

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

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

29 <p>15.62 = 243.36 which too less</p>

28 <p>15.62 = 243.36 which too less</p>

30 <p>Go to the next number 15.7, 15.72 = 246.49 which is too high.</p>

29 <p>Go to the next number 15.7, 15.72 = 246.49 which is too high.</p>

31 <p>So, √245 = 15.6525</p>

30 <p>So, √245 = 15.6525</p>

32 <h3>Subtraction Method</h3>

31 <h3>Subtraction Method</h3>

33 <p>The<a>subtraction</a>method includes subtracting consecutive<a>odd numbers</a>from 245 to see how many steps we need to reach zero. However, since 245 is not a perfect square, we cannot exactly reach 0. </p>

32 <p>The<a>subtraction</a>method includes subtracting consecutive<a>odd numbers</a>from 245 to see how many steps we need to reach zero. However, since 245 is not a perfect square, we cannot exactly reach 0. </p>

34 <p>245 -1 =244</p>

33 <p>245 -1 =244</p>

35 <p>244-3=241</p>

34 <p>244-3=241</p>

36 <p>241-5=236</p>

35 <p>241-5=236</p>

37 <p>As we did not get zero, we understand that 245 is not a perfect square. </p>

36 <p>As we did not get zero, we understand that 245 is not a perfect square. </p>

38 <h2>Common Mistakes and How to Avoid Them in the Square Root of 245</h2>

37 <h2>Common Mistakes and How to Avoid Them in the Square Root of 245</h2>

39 <p>While learning about square roots, students may likely make mistakes, to avoid them a few mistakes with solutions are given below: </p>

38 <p>While learning about square roots, students may likely make mistakes, to avoid them a few mistakes with solutions are given below: </p>

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40 <h3>Problem 1</h3>

41 <p>If, x²=245, find the value of x.</p>

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

43 <p>If, x2=245</p>

44 <p>Then, </p>

45 <p>x= √245 </p>

46 <h3>Explanation</h3>

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

48 <p>x=√ 5x7x7 </p>

49 <p>x=7√5</p>

50 <p>So the value of x is 7√5.</p>

51 <p>Well explained 👍</p>

52 <h3>Problem 2</h3>

53 <p>Verify if √245 is greater than 15.</p>

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

55 <p>First, approximate √245 :</p>

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

57 <p>√245 = √5x49 = 7√5</p>

58 <p>Since 5 = 2.236</p>

59 <p>7√5 = 7 × 2.236 =15.652</p>

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

61 <p>√245 > 15</p>

62 <h3>Explanation</h3>

63 <p>The approximation of √245 shows us that it is greater than 15.</p>

64 <p>Well explained 👍</p>

65 <h3>Problem 3</h3>

66 <p>Express the square root of 245 in the simplest radical form.</p>

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

68 <p>√ 245 = 5 × 72</p>

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

70 <p>√245 = √5x7x7 </p>

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

72 <p>√245 = 7√5 </p>

73 <p>So, the value is 7√5 .</p>

74 <h3>Explanation</h3>

75 <p>The square root of 245 in the simplest form is 7√5</p>

76 <p>Well explained 👍</p>

77 <h3>Problem 4</h3>

78 <p>Solve: 10/√245</p>

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

80 <p> To simplify, 10/ √245 We multiply the number in the denominator with the numerator and the denominator, which is called rationalizing. </p>

81 <h3>Explanation</h3>

82 <p>10/ √245 /x √245 / √245 = 10√245 / 245 , 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 √245 x √245 = 245. After rationalizing, we get, 10 x √245 /245 </p>

83 <p>Well explained 👍</p>

84 <h2>FAQs on 245 Square Root</h2>

85 <h3>1.What is the perfect square factor of 245?</h3>

86 <p>To find the perfect square of a number, we multiply the number by itself. 245 is not a perfect square but to make it a perfect square, the least number that should be multiplied is 5. </p>

87 <h3>2.Is 3 divisible by 245?</h3>

88 <p>The<a>sum</a>of the digits of 245, 2+4+5=11. As 11 is not divisible by 3. No, 245 is not divisible by 3. </p>

89 <h3>3.Is √245 an irrational number?</h3>

90 <p>Yes, √245 is an irrational number, as it cannot be written in p/q form, √245 =√245 /1 where p is not an<a>integer</a>.</p>

91 <h3>4.Is 245 a perfect Square?</h3>

92 <p>No, 245 is not a perfect square. It cannot be written as two equal numbers. </p>

93 <h3>5.What is 245 divisible by?</h3>

94 <p>The numbers 1,5,7,35,49,245 divide 245. </p>

95 <h2>Important Glossaries for Square Root of 245</h2>

96 <ul><li><strong>Irrational number:</strong>A number that cannot be written in the form of a ratio or fraction. For example, √245 is an irrational number.</li>

97 </ul><ul><li><strong>Exponent form:</strong>Writing the square root of a number in the form of degree or powers. For example, 2451/2 ≅ 4.7958</li>

98 </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>

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

100 <p>▶</p>

101 <h2>Jaskaran Singh Saluja</h2>

102 <h3>About the Author</h3>

103 <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>

104 <h3>Fun Fact</h3>

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