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. That leaves us with a problem, if -12 * -12 = 144 what is the square root of -144? Also tells you if the entered number is a perfect square. The value of the square root of 144 is equal to 12. For example, 9, 36, 144 etc are perfect squares. Square root calculator and perfect square calculator. Vedantu academic counsellor will be calling you shortly for your Online Counselling session. The square Root of 144 in its simplest form means to get the number 144 inside the radical √ as low as possible. 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. The less obvious square root of 144 is -12. Thus there are two square roots of any positive number that is the positive and negative root. 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. Well, 3 × 3 = 9 and 4 × 4 = 16, so we can guess the answer is between 3 and 4. Pro Lite, Vedantu For example, 12 ×12= 144. Pro Lite, Vedantu Pull terms out from under the radical, assuming positive real numbers. Tap for more steps... Rewrite as . 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. Hence, considering 1 as quotient, dividend and divisor, we get the remainder equals to 0. Pro Lite, CBSE Previous Year Question Paper for Class 10, CBSE Previous Year Question Paper for Class 12. Hence, we get quotient as 12 and this will be our final answer. The square root of 144 is a quantity (q) that when multiplied by itself will equal 144. So the expresion $\sqrt{144}$ evaluates to the positive root 12. 1. Also tells you if the entered number is a perfect square. The square root of any natural number is a value that is represented in the form of x = \[\sqrt{b}\]. This method can only be used if the number given is a perfect square. The square root of a number can also be calculated using the long division method. We call this the square root of 144 in radical form. Hence, we can see the square root value of 144 is 12. Example: what is √10? Find the square root, or the two roots, including the principal root, of positive and negative real numbers. Rewrite as . Calculating Square Roots. = \[\sqrt{2\times2\times2\times2\times3\times3}\], = \[\sqrt{(2 \times 2 \times 3 \times 3)}\], = \[\bar{2\ast2}\] \[\ast\] \[\bar{3\ast3}\] \[\ast\] \[\bar{3\ast3}\], 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 The Square Root of 144, \[\sqrt{144}\] is 12. 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. 144 is a perfect square, which means that you can simply calculate the square Root of 144 to get the answer. Omit the first digit i.e.1 and leave the remaining two digits i.e. We refer to this convention by saying $\sqrt{x}$ is the principal square Pull terms out from under the radical, assuming positive real numbers. By using this website, you agree to our Cookie Policy. In radical form, it is denoted as √144 = 12. Free Square Roots calculator - Find square roots of any number step-by-step. 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. Now, we will carry forward the other two numbers i..e. 44. 44. There are two methods to determine the square root value of 144. 3. 12 times 12 equals 144. It is a value which when multiplied by itself gives the number 144. \[\sqrt{36}\] = \[\sqrt{(2 \times 2 \times 3 \times 3)}\]. Definition of square root. On the other hand, 72 is a composite number that can easily be factored further. 324 can also be written as 2 ×2 ×3 × 3 × 3 ×3, Therefore, \[\sqrt{324}\] = \[\bar{2\ast2}\] \[\ast\] \[\bar{3\ast3}\] \[\ast\] \[\bar{3\ast3}\]. The number inside the square root is known as radicand. By using this website, you agree to our Cookie Policy. 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. Tap for more steps... Rewrite as . Any natural or whole numbers (excluding 0) when multiplied by any prime numbers give composite numbers. Therefore, the prime factors of 144 = 2 × 2 × 2 × 2 × 3 × 3, If we take the square root of both the sides, we get, \[\sqrt{144}\] = \[\sqrt{2\times2\times2\times2\times3\times3}\]. 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. Square root of 144 is 12. It is easy to work out the square root of a perfect square, but it is really hard to work out other square roots. For example, 2 and 72 are two numbers which when multiplied together obtains the result 144. What is the Meaning of Prime Factorization? Evaluate square root of 144/25. 1. Sorry!, This page is not available for now to bookmark. We know the square root of digit 1 is always 1. The two methods to determine the square root value of 144 are Prime Factorization Method and Long Division Method. Find the Square Root of 36 By the Prime Factorization Method. Simplify the denominator. 1. In Mathematics, the square root of 144 is a value which when multiplied by itself gives the result 144. 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. A number calculated by squaring a number is considered as a perfect square. 2. Square root calculator and perfect square calculator. A perfect square is an integer whose square root is always an integer . We can see 2 pairs of 2 and 1 pair of 3 in the above given prime factors of 144. It is termed as perfect square since 12 is a rational number. What is square root? Find the square root, or the two roots, including the principal root, of positive and negative real numbers. Try to remember them up to 12. For Example, 5 × 5 = 25 and it can be said that the square root of a number 25 is 5. Calculate the positive principal root and negative root of positive real numbers. For example, 12 ×12= 144. Learn more Accept. 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. We can also write it as x² = b. Hence, we can see the square root value of 144 is 12. It is written in the radical form as \[\sqrt{144}\] = 12. This website uses cookies to ensure you get the best experience. Therefore, the factors of 144 can be written as 2 ×2 × 2 × 2 × 3 × 3 × 1. Note a negative times a negative is a positive so -12 * -12 = 144. According to the equation given above, we can state that the square root of natural number 144 is 12. 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. What are the Different Steps to Calculate the Factors of 144? Find the Square Root of 324 Using the Prime Factorization Method. Hence, it is concluded that the square root of any number is equal to a number which when multiplied by itself obtains back the original numbers.
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