Now, when we multiply an irrational number,\[\sqrt{2}\], by a rational number, 2, the result so obtained, 2\[\sqrt{2}\], is an irrational number. Therefore, \[\sqrt{8}\] =\[\sqrt{2^{3}}\] or \[\sqrt{2}\] x \[\sqrt{2}\] x \[\sqrt{2}\]. Hence the answer to the root of 8 lies between the numbers 2 and 3. Any square root is represented by the square root symbol √. Now, when we multiply an irrational number,\[\sqrt{2}\], by a rational number, 2, the result so obtained, 2\[\sqrt{2}\], is … Let us estimate the value of the square roots now. The number underneath this radical symbol is known as radicand. We call this the square root of 8 in radical form. Then, we take that value and multiply by itself 3 times. The square root of the resulting number, x\[^{2}\], is expressed as \[\sqrt{x^{2}}\], that is, x. Then you can break the factors (which are smaller numbers) into their subsequent prime factors. For example, the principal square root of 9 is 3, denoted √9 = 3, because 32 = 3 ^ 3 = 9 and 3 is non-negative. Even though 8 is not a prime number, yet, when we take its square root, we get 2, as its only prime factor. So, you can easily find the cube root of 8 which is denoted as \[\sqrt[3]{8}\]= 2. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. To estimate the square root of a perfect square, we always implement the first method. For example, 4 and -4 are square roots of 16 because 4² = (-4)² = 16. A radical is also in simplest form when the radicand is not a fraction. When you manually find the value of root 8, you get 2√2. Consider any two other numbers, say, n and m in such a way that n. . The square root of eight √8 = 2.8284271247462 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. According to Math Warehouse, the square root of eight is 2.82. For example, 2 is the square root of 4, because 2x2=4. Now, take out 4 from the radical since √4 value is 2. √ 8 = q × q = q 2 What is the Exact Value of the Root of 8 in Decimal Form? For simplifying the root 8 value, first, write √8 as 22 x 2. Although it is easy to find the root 8 value by using a calculator, you should know how to find its value manually. Well, did you know the answer to the square root of 8 to the power 3? Root of √4=2 which results into 2√2. This symbol is known as the radical symbol or simply radix. Taking the whole root of the value 22 x 2, you get √4 x √2. Then multiply this value by itself for 3 times to get the answer. 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. As you can see the radicals are not in their simplest form. But, since √2 leads you to a decimal number, it becomes tedious to find the exact value of √2. 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. However, since the square of 3 equals to 9 which is larger than 8, the root 8 value lies in between the number 2.8 and 2.9. A whole number with a square root that is also a whole number is called a perfect square. The square root radical is simplified or in its simplest form only when the radicand has no square factors left. In this way, the calculation becomes easier and less time-consuming. The square root of 8 is a quantity (q) that when multiplied by itself will equal 8. The square root of 8, denoted by \[\sqrt{8}\], is the number whose square gives you the number 8. that are perfect squares and whose squares are easy to find. However, to calculate the square root of a number, which is not a perfect square, in decimal, the division method is used. Pro Lite, CBSE Previous Year Question Paper for Class 10, CBSE Previous Year Question Paper for Class 12. Now, 8 = 2\[^{3}\], that is, 2x2x2. This value is called surd since you cannot simplify this further. \[\sqrt{16}\] = 4, as you know 4 x 4 = 16. A faster way to estimate the square root of a bigger number is to determine its range. Pro Lite, Vedantu USING OUR SERVICES YOU AGREE TO OUR USE OF. The square root of 8 is 2\[\sqrt{2}\]. There are two methods of estimating square roots, one that uses the prime factors of the number, and the other devises a division method. A square root of a number is a number that, when it is multiplied by itself (squared), gives the first number again. To solve the problem, we need to take the square root of 8. The square root of 8 is 2\[\sqrt{2}\]. The precise answer of the square root of 8 is 2.82842712475. this is much closer to the answer that we estimated. In a simpler for, \[\sqrt{8}\] is written as \[2\sqrt{2}\]. You can use these values for your calculations. However, since the square of 3 equals to 9 which is larger than 8, the root 8 value lies in between the number 2.8 and 2.9. For example, 4 has two square roots: 2 and -2. The radicand is the number or expression underneath the radical sign, in this example 9. For example, you are calculating the square root of x. The justification for taking out the square root of any number is this theorem to help simplify √a*b = √a * √b. Now, since you know the value of root 8, let us find out how to calculate its value here. Do you know what the square root of 8 to the power of 3 is? However, there are a few numbers like 4, 9, 16, etc. In this article, we will learn about the square root of 8 and how to find the root 8 value. However, 8 is a perfect cube of the number 2 since 2 x 2 x 2 = 8. Now extract and take out the square root √4 * √2. The radicand no longer has any square factors. = 9. For example, 4 and -4 are square roots of 16 because 4² = (-4)² = 16. 2. For example, you are calculating the square root of x. Therefore, the answer to the square root of 8 to power 3 is (2.828) x 3 = 22.627. The square root of eight √8 = 2.8284271247462. Here is a chart of the square roots of numbers from 1 to 100 for your reference. The square root of a bigger number can also be calculated by expressing it as the product of its factors, first. The square of a number, x, is obtained when it is multiplied by itself. Simplifying the value of root 8 is simple and easy to follow. 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 This symbol is known as the radical symbol or radix. The square of a number, x, is obtained when it is multiplied by itself. The square root of 8 in mathematical form is written with the radical sign like this √8. Hence, the exact value of root 8 in the decimal form is √8 = 2.82842712475. 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. If you follow these easy steps, you will be able to simplify it easily. The exact value of root 8 can be calculated with the help of a calculator. A number bigger than zero has two square roots: one is positive (bigger than zero) and the other is negative (smaller than zero). Vedantu academic counsellor will be calling you shortly for your Online Counselling session. To find the value of √8, you have to first express the number 8 as a product of its prime factors.