3. The square root of 144 is a quantity (q) that when multiplied by itself will equal 144. We call this the square root of 144 in radical form. If two numbers are given, then the HCF (highest common factor ) will be the largest factor comprising both the numbers whereas the LCM (Least Common Multiple) will be the smallest common multiple existing in both the numbers. This method is primarily used to find the square roots of imperfect squares and large numbers which cannot be calculated using the prime factorization method. For example, 9, 36, 144 etc are  perfect squares. What is the Meaning of Prime Factorization? Mod the number 36 into prime factorization using the method of synthetic division. Square root calculator and perfect square calculator. Area of the square = Side x Side (formula) Area = 144 sq.m (Side)^2= 144 ( given) Side = + or - 12 ( taking square root on both sided) Discarding negative sign , side is 12 m Ans : … We refer to this convention by saying $\sqrt{x}$ is the principal square Tap for more steps... Rewrite as . Note a negative times a negative is a positive so -12 * -12 = 144. Pull terms out from under the radical, assuming positive real numbers. That leaves us with a problem, if -12 * -12 = 144 what is the square root of -144? For example, 12 ×12= 144. Hence, 72 can be factorized as 2 ×2× 2 × 3 × 3 × 1. Sorry!, This page is not available for now to bookmark. \[\sqrt{36}\] =  \[\sqrt{(2 \times 2 \times 3 \times 3)}\]. For example, 2 and 72 are two numbers which when multiplied together obtains the result 144. We know the square root of digit 1 is always 1. Free Square Roots calculator - Find square roots of any number step-by-step. Omit the first digit i.e.1 and leave the remaining two digits i.e. 144 is a perfect square, which means that you can simply calculate the square Root of 144 to get the answer. There are two methods to determine the square root value of 144. Simplify the numerator. A perfect square is an integer whose square root is always an integer . Vedantu academic counsellor will be calling you shortly for your Online Counselling session. Example: what is √10? In Mathematics, the square root of 144 is a value which when multiplied by itself gives the result 144. Find the Square Root of 12544 Using the Long Division Method. This website uses cookies to ensure you get the best experience. Pull terms out from under the radical, assuming positive real numbers. Simplify the denominator. The prime factorization method can easily be used as we have studied about prime factors in our previous classes. 1. The square root of one hundred and forty-four √144 = 12 How To Calculate Square Roots In mathematics, a square root of a number a is a number y such that y² = a, in other words, a number y whose square (the result of multiplying the number by itself, or y * y) is a. It is written in the radical form as \[\sqrt{144}\] = 12. Definition of square root. Find the Square Root of 324 Using the Prime Factorization Method. Hence, we can see the square root value of 144 is 12. Hence, we can see the square root value of 144 is 12. The square root of any natural number is a value that is represented in the form of x = \[\sqrt{b}\]. Therefore, the prime factors of 144 = 2 × 2 × 2 × 2 × 3 × 3, If we take the square root of both the sides, we get, \[\sqrt{144}\]  =  \[\sqrt{2\times2\times2\times2\times3\times3}\]. Thus there are two square roots of any positive number that is the positive and negative root. Free Square Roots calculator - Find square roots of any number step-by-step This website uses cookies to ensure you get the best experience. What is square root? Calculating Square Roots. For example, the prime factors of a number 126 will be 2, 3 ,and 7 as 2 × 3 × 7 = 126 and 2,3,and 7 are prime numbers. 1. Pro Lite, Vedantu The less obvious square root of 144 is -12. The two methods to determine the square root value of 144 are Prime Factorization Method and Long Division Method. Rewrite as . Therefore, the factors of 144 can be written as 2 ×2 × 2 × 2 × 3 × 3 × 1. There are two methods to determine the square root value of 144. Square root calculator and perfect square calculator. The two methods to find the square root of a given number are: In the Prime factorization method, we generally determine the prime factors of a given number. A number calculated by squaring a number is considered as a perfect square. The square root of a number can also be calculated using the long division method. By using this website, you agree to our Cookie Policy. It is written in the radical form as \[\sqrt{144}\] = 12. Well, 3 × 3 = 9 and 4 × 4 = 16, so we can guess the answer is between 3 and 4. The number inside the square root is known as radicand. For example, 12 is the square root of 144 because 12 2 = 12•12 = 144, -12 is square root of 144 because (-12) 2 = (-12)•(-12) = 144. Find the square root, or the two roots, including the principal root, of positive and negative real numbers. Now, we will carry forward the other two numbers i..e. 44. Pro Lite, Vedantu Learn more Accept. Hence, considering 1 as quotient, dividend and divisor, we get the remainder equals to 0. Evaluate square root of 144/25. Tap for more steps... Rewrite as . According to the equation given above, we can state that the square root of natural number 144 is  12. For example, 12 ×12= 144. Square root of 144 is 12. The Prime Factorization method is also used in calculating HCF and LCM of any given set of numbers. Also tells you if the entered number is a perfect square. A square root of a number 'a' is a number x such that x 2 = a, in other words, a number x whose square is a. Below are some of the steps which show the way to calculate square root of 144 using the long division method. 1. In radical form, it is denoted as √144 = 12. The number 44 will be considered as dividend and we will further add 1 to the divisor to get our next divisor i.e.1 + 1= 2. At the end, mention all the unique numbers that are obtained as factors. =  \[\sqrt{2\times2\times2\times2\times3\times3}\], =  \[\sqrt{(2 \times 2 \times 3 \times 3)}\], = \[\bar{2\ast2}\] \[\ast\] \[\bar{3\ast3}\] \[\ast\] \[\bar{3\ast3}\], NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots, NCERT Solutions for Class 8 Maths Chapter 6- Squares and Square Roots Exercise 6.4, NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots in Hindi, NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots (EX 6.1) Exercise 6.1, NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots (EX 6.3) Exercise 6.3, NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots (EX 6.2) Exercise 6.2, NCERT Solutions for Class 7 Science Chapter 7 Weather, Climate and Adaptations of Animals to Climate, NCERT Solutions for Class 12 Chemistry Chapter 6 General Principles and Processes of Isolation of Elements in Hindi, NCERT Solutions for Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles, NCERT Solutions for Class 7 Science Chapter 7 Weather, Climate and Adaptations of Animals to Climate In Hindi, CBSE Class 8 Maths Chapter 6 - Squares and Square Roots Formulas, CBSE Class 8 Maths Revision Notes Chapter 6 - Squares and Square Roots, CBSE Class 7 Science Revision Notes Chapter 7 - Weather, Climate and Adaptations of Animals to Climate, Class 9 Maths Revision Notes for Areas of Parallelograms and Triangles of Chapter 9, Class 10 Maths Revision Notes for Introduction to Trigonometry of Chapter 8, Class 10 Maths Areas Related to Circles Notes for Circles of Chapter 12, Vedantu Is denoted as √144 = 12, dividend and divisor, we get quotient as 12 and will... 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