In Mathematics, the square root of 144 is a value which when multiplied by itself gives the result 144. Hence, we can see the square root value of 144 is 12. We can also write it as x² = b. A perfect square is an integer whose square root is always an integer . Therefore, the factors of 144 can be written as 2 ×2 × 2 × 2 × 3 × 3 × 1. The square Root of 144 in its simplest form means to get the number 144 inside the radical √ as low as possible. Pro Lite, Vedantu Evaluate square root of 144/25. For example, 2 and 72 are two numbers which when multiplied together obtains the result 144. It is written in the radical form as \[\sqrt{144}\] = 12. The Square Root of 144, \[\sqrt{144}\]  is 12. A function can only produce a single result. The two methods to determine the square root value of 144 are Prime Factorization Method and Long Division Method. Also tells you if the entered number is a perfect square. Learn more Accept. Find the square root, or the two roots, including the principal root, of positive and negative real numbers. 2. The number inside the square root is known as radicand. Tap for more steps... Rewrite as . Simplify the denominator. 144 is a perfect square, which means that you can simply calculate the square Root of 144 to get the answer. Find the Square Root of 324 Using the Prime Factorization Method. The prime factorization method can easily be used as we have studied about prime factors in our previous classes. Pro Lite, Vedantu \[\sqrt{36}\] =  \[\sqrt{(2 \times 2 \times 3 \times 3)}\]. Hence, we can say that prime factorization is generally implemented on composite numbers. We refer to this convention by saying $\sqrt{x}$ is the principal square Calculate the positive principal root and negative root of positive real numbers. 1. Thus there are two square roots of any positive number that is the positive and negative root. On the other hand, 72 is a composite number that can easily be factored further. Pull terms out from under the radical, assuming positive real numbers. 12 times 12 equals 144. That leaves us with a problem, if -12 * -12 = 144 what is the square root of -144? By using this website, you agree to our Cookie Policy. As we know, that 2 is the prime number which has two prime factors i.e, 2 and 1 and it cannot be factored further. Calculate the positive principal root and negative root of positive real numbers. The square root of 144 is a quantity (q) that when multiplied by itself will equal 144. There are two methods to determine the square root value of 144. While -12 is "a square root" of 144, the square root operation here denotes a function from nonnegative real numbers to nonnegative real numbers. 324 can also be written as 2 ×2 ×3 × 3 × 3 ×3, Therefore, \[\sqrt{324}\] = \[\bar{2\ast2}\] \[\ast\] \[\bar{3\ast3}\] \[\ast\] \[\bar{3\ast3}\]. Hence, 72 can be factorized as 2 ×2× 2 × 3 × 3 × 1. We call this the square root of 144 in radical form. It is termed as perfect square since 12 is a rational number. Hence, we get quotient as 12 and this will be our final answer. Mod the number 36 into prime factorization using the method of synthetic division. Pro Lite, CBSE Previous Year Question Paper for Class 10, CBSE Previous Year Question Paper for Class 12. 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. Definition of square root. Note a negative times a negative is a positive so -12 * -12 = 144. Square root of 144 definition The square root of 144 in mathematical form is written with the radical sign like this √144. Try to remember them up to 12. 2. So the expresion $\sqrt{144}$ evaluates to the positive root 12. This method can only be used if the number given is a perfect square. It is a value which when multiplied by itself gives the number 144. What is square root? Any natural or whole numbers (excluding 0) when multiplied by any prime numbers give composite numbers. 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. In this step, we will fix 2 with 2 and multiply the divisor 22 by 2 such as 22 × 2 to get the dividend 44. Find the Square Root of 12544 Using the Long Division Method. In this article, we will learn both the methods that will help the students to find the square root of any numbers in a simpler and fastest way. The different steps to calculate the factors of 144 are given below: Find any two numbers which when multiplied together obtains the original number 144. The long division method of finding the square root is useful and the square root of any number can be found out speedily. It implies that x is the square root of b , where b is any natural number. Below are some of the steps which show the way to calculate square root of 144 using the long division method. The Prime Factorization method is also used in calculating HCF and LCM of any given set of numbers. The square root of a number can also be calculated using the long division method. A number calculated by squaring a number is considered as a perfect square. According to the equation given above, we can state that the square root of natural number 144 is  12. =  \[\sqrt{2\times2\times2\times2\times3\times3}\], =  \[\sqrt{(2 \times 2 \times 3 \times 3)}\], = \[\bar{2\ast2}\] \[\ast\] \[\bar{3\ast3}\] \[\ast\] \[\bar{3\ast3}\], 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 To calculate the value to root 144 without using a calculator, there are two methods: one is the prime factorisation and another is the long division method. Square root calculator and perfect square calculator. For Example, 5 × 5 = 25 and it can be said that the square root of a number 25 is 5. Well, 3 × 3 = 9 and 4 × 4 = 16, so we can guess the answer is between 3 and 4. The square root of any natural number is a value that is represented in the form of x = \[\sqrt{b}\]. As the last digit is 4, then either the  square of 2 or 4 can have the last digit 4. For example, 12 ×12= 144. Sorry!, This page is not available for now to bookmark. Hence, considering 1 as quotient, dividend and divisor, we get the remainder equals to 0. 44. 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. It is written in the radical form as \[\sqrt{144}\] = 12. The value of the square root of 144 is equal to 12. We know the square root of digit 1 is always 1. 1. 1. What are the Different Steps to Calculate the Factors of 144? 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 : … 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. Prime Factorization is a method of determining prime factors of a given number i.e the two prime numbers which when multiplied together give back an original number. The result can be shown in multiple forms. Vedantu academic counsellor will be calling you shortly for your Online Counselling session. Also tells you if the entered number is a perfect square. Tap for more steps... Rewrite as . For example, 9, 36, 144 etc are  perfect squares. 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. For example, 12 ×12= 144. Square root of 144 is 12. Find the Square Root of 36 By the Prime Factorization Method. 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