Every non-negative real number a has a unique non-negative square root, called the principal square root, which is denoted by √a, where √ is called the radical sign or radix. = 9. Now, you can say that √x is a number that lies in between the numbers n and m. In this way, it will become easier to estimate the square root of bigger numbers. However, to calculate the square root of a number, which is not a perfect square, in decimal, the division method is used. Now, we know that \[\sqrt{2}\] = 1.41421... A faster way to estimate the square root of a bigger number is to determine its range. The value of root 8 is \[\sqrt{8}\] = 2.82842712475, If you consider the first three decimal places \[\sqrt{8}\] = 2.828. The square root of 8 is 2\[\sqrt{2}\]. What is the Exact Value of the Root of 8 in Decimal Form? Sorry!, This page is not available for now to bookmark. The number underneath this radical symbol is known as radicand. Although it is easy to find the root 8 value by using a calculator, you should know how to find its value manually. You can use these values for your calculations. The only square root of zero is zero. We call this the square root of 8 in radical form. 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 8 Comparing Quantities (EX 8.1) Exercise 8.1, 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 8 Comparing Quantities (EX 8.3) Exercise 8.3, NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.2, NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots (EX 6.2) Exercise 6.2, NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities, 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 8 Maths Revision Notes Chapter 8 - Comparing Quantities, CBSE Class 8 Maths Chapter 16 - Playing with Numbers Formulas, CBSE Class 8 Maths Chapter 15 - Introduction to Graphs Formulas, CBSE Class 8 Science Revision Notes Chapter 8 - Cell - Structure and Functions, Vedantu Hence the answer to the root of 8 lies between the numbers 2 and 3. The square root of a bigger number can also be calculated by expressing it as the product of its factors, first. For you to remember, 22= 4, and 32= 9. The square root of 8 in mathematical form is written with the radical sign like this √8. Then you can break the factors (which are smaller numbers) into their subsequent prime factors. According to Math Warehouse, the square root of eight is 2.82. A radical is also in simplest form when the radicand is not a fraction. Any square root is represented by the square root symbol √. All radicals are now simplified. For example, 4 has two square roots: 2 and -2. In this way, the calculation becomes easier and less time-consuming. The square root of a number is represented by the symbol √. If you follow these easy steps, you will be able to simplify it easily. To find the value of √8, you have to first express the number 8 as a product of its prime factors. Now, since you know the value of root 8, let us find out how to calculate its value here. Pro Lite, Vedantu Simplifying the value of root 8 is simple and easy to follow. USING OUR SERVICES YOU AGREE TO OUR USE OF. A whole number with a square root that is also a whole number is called a perfect square. So, you can easily find the cube root of 8 which is denoted as \[\sqrt[3]{8}\]= 2. However, there are a few numbers like 4, 9, 16, etc. Only numbers bigger than or equal to zero have real square roots. \[\sqrt{16}\] = 4, as you know 4 x 4 = 16. Let us estimate the value of the square roots now. A square root of a number is a number that, when it is multiplied by itself (squared), gives the first number again. Pro Lite, CBSE Previous Year Question Paper for Class 10, CBSE Previous Year Question Paper for Class 12. For example, 2 is the square root of 4, because 2x2=4. This value is called surd since you cannot simplify this further. The precise answer of the square root of 8 is 2.82842712475. this is much closer to the answer that we estimated. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. In a simpler for, \[\sqrt{8}\] is written as \[2\sqrt{2}\]. It would be easier for you to find the value of root 8 now with this easy method. The square root of eight √8 = 2.8284271247462. To estimate the square root of a perfect square, we always implement the first method. In this article, we will learn about the square root of 8 and how to find the root 8 value. Then, we take that value and multiply by itself 3 times. The justification for taking out the square root of any number is this theorem to help simplify √a*b = √a * √b. Hence the answer to the root of 8 lies between the numbers 2 and 3. √ 8 = q × q = q 2 Now, you can say that √x is a number that lies in between the numbers n and m. In this way, it will become easier to estimate the square root of bigger numbers. This symbol is known as the radical symbol or simply radix. For example, 4 and -4 are square roots of 16 because 4² = (-4)² = 16. Now extract and take out the square root √4 * √2. So essentially, square root of 8 to the power of 3 = (2.828 x 2.828 x 2.828) = 22.627. Here is a chart of the square roots of numbers from 1 to 100 for your reference. Hence, the square root of 8, i.e.,\[\sqrt{8}\], is an irrational number 2\[\sqrt{2}\]. The square root of 8 is a quantity (q) that when multiplied by itself will equal 8. Even though 8 is not a prime number, yet, when we take its square root, we get 2, as its only prime factor. The radicand no longer has any square factors. The square root of 8, denoted by \[\sqrt{8}\], is the number whose square gives you the number 8. The square root radical is simplified or in its simplest form only when the radicand has no square factors left. Hence, the exact value of root 8 in the decimal form is √8 = 2.82842712475. For example, 4 and -4 are square roots of 16 because 4² = (-4)² = 16.