Simplify Square Root of 108 Show
Step 1: List Factors List the factors of 108 like so:1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108 Step 2: Find Perfect Squares Identify the perfect squares* from the list of factors above: 1, 4, 9, 36 Step 3: Divide Divide 108 by the largest perfect square you found in the previous step:108 / 36 = 3 Step 4: Calculate Calculate the square root of the largest perfect square:√36 = 6 Step 5: Get Answer Put Steps 3 and 4 together to get the square root of 108 in its simplest form:Simplify Square Root Calculator Please enter another Square Root for us to simplify: Decimal Form Square Root of 108 in Decimal form rounded to nearest 5 decimals: 10.3923 Exponent Form Square Root of 108 written with Exponent instead of Radical:108½ = 6 x 3½ Simplify Square Root of 109 * List of Perfect Squares Copyright | Privacy Policy | Disclaimer | Contact Square root of 108 definition The square root of 108 in mathematical form is written with the radical sign like this √108. We call this the square root of 108 in radical form. The square root of 108 is a quantity (q) that when multiplied by itself will equal 108. √108 = q × q = q2 Is 108 a perfect square? 108 is a perfect square if the square root of 108 equals a whole number. As we have calculated further down on this page, the square root of 108 is not a whole number. 108 is not a perfect square. Is the square root of 108 rational or irrational? The square root of 108 is a rational number if 108 is a perfect square. It is an irrational number if it is not a perfect square. Since 108 is not a perfect square, it is an irrational number. This means that the answer to "the square root of 108?" will have an infinite number of decimals. The decimals will not terminate and you cannot make it into an exact fraction. √108 is an irrational number Can the square root of 108 be simplified? You can simplify 108 if you can make 108 inside the radical smaller. We call this process "to simplify a surd". The square root of 108 can be simplified. √108 = 6√3 How to calculate the square root of 108 with a calculator The easiest and most boring way to calculate the square root of 108 is to use your calculator! Simply type in 108 followed by √x to get the answer. We did that with our calculator and got the following answer with 9 decimal numbers: √108 ≈ 10.392304845 How to calculate the square root of 108 with a computer If you are using a computer that has Excel or Numbers, then you can enter SQRT(108) in a cell to get the square root of 108. Below is the result we got with 13 decimals. We call this the square root of 108 in decimal form. SQRT(108) ≈ 10.3923048454133 What is the square root of 108 rounded? The square root of 108 rounded to the nearest tenth, means that you want one digit after the decimal point. The square root of 108 rounded to the nearest hundredth, means that you want two digits after the decimal point. The square root of 108 rounded to the nearest thousandth, means that you want three digits after the decimal point. 10th: √108 ≈ 10.4 100th: √108 ≈ 10.39 1000th: √108 ≈ 10.392 What is the square root of 108 as a fraction? Like we said above, since the square root of 108 is an irrational number, we cannot make it into an exact fraction. However, we can make it into an approximate fraction using the square root of 108 rounded to the nearest hundredth. √108 ≈ 10.39/1 ≈ 1039/100≈ 10 39/100 What is the square root of 108 written with an exponent? All square roots can be converted to a number (base) with a fractional exponent. The square root of 108 is no exception. Here is the rule and the answer to "the square root of 108 converted to a base with an exponent?": √b = b½ √108 = 108½ How to find the square root of 108 by long division method Here we will show you how to calculate the square root of 108 using the long division method with one decimal place accuracy. This is the lost art of how they calculated the square root of 108 by hand before modern technology was invented. Step 1) Set up 108 in pairs of two digits from right to left and attach one set of 00 because we want one decimal:Step 2) Starting with the first set: the largest perfect square less than or equal to 1 is 1, and the square root of 1 is 1. Therefore, put 1 on top and 1 at the bottom like this: Step 3) Calculate 1 minus 1 and put the difference below. Then move down the next set of numbers. Step 4) Double the number in green on top: 1 × 2 = 2. Then, use 2 and the bottom number to make this problem: 2? × ? ≤ 8 The question marks are "blank" and the same "blank". With trial and error, we found the largest number "blank" can be is 0. Replace the question marks in the problem with 0 to get: 20 × 0 = 0. Now, enter 0 on top, and 0 at the bottom:Step 5) Calculate 8 minus 0 and put the difference below. Then move down the next set of numbers. Step 6) Double the number in green on top: 10 × 2 = 20. Then, use 20 and the bottom number to make this problem: 20? × ? ≤ 800 The question marks are "blank" and the same "blank". With trial and error, we found the largest number "blank" can be is 3. Now, enter 3 on top:
Square Root of a Number Please enter another number in the box below to get the square root of the number and other detailed information like you got for 108 on this page. Notes Remember that negative times negative equals positive. Thus, the square root of 108 does not only have the positive answer that we have explained above, but also the negative counterpart. We often refer to perfect square roots on this page. You may want to use the list of perfect squares for reference. Square Root of 109 Here is the next number on our list that we have equally detailed square root information about. Copyright | Privacy Policy | Disclaimer | Contact
The value of root 108 is 10.392. Note that the square root of a number x is denoted by √x, so the square root of 108 can be written as √108. In this section, we will learn how to calculate the square root of 108. But before we do that, here are the few things to remember about the number 108. • 108 is a composite even number. • The number 108 is divisible by 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54 and 108. • As 108=9×12, the number 108 is equal to 9 dozen. Also Read: Properties of square roots Simplify square root of 108?What is the square root of 108 in simplest radical form? We will express 108 as a product of perfect squares or as a product of a perfect square and a non-perfect square. Note that 108=36×3. Observe that here 36 is a perfect square number whose square root is 6 and the number 3 is a non-perfect square. Taking square root on both sides of 108 = 36×3, we get that $\sqrt{108}=\sqrt{36 \times 3}$ $=\sqrt{36} \times \sqrt{3}$ $[\because \sqrt{a \times b}=\sqrt{a} \times \sqrt{b}]$ $=6 \times \sqrt{3}=6\sqrt{3}$ So the simplest radical form of the square root of 108 is 6√3. Is 108 a perfect square number?We have computed that √108=6√3. So the square root of 108 is not an integer. This makes that 108 is not a perfect square number. Therefore, 108 is a non-perfect square number. So we deduce that its square root √108 is a quadratic surd. Is Square root of 108 Rational?As √108=6√3 and the square root of 3 is not a rational number, so we deduce that the square root of 108 is not a rational number. Note that √108 is an irrational number. Also Read:
What is the value of root 108?Note that the simplest radical form of square root of 108 is 6√3. Now using the fact that the value of √3 is 1.732, we get that √108 = 6√3 = 6 × 1.732 = 10.392 So 10.392 is the value of the square root of 108. Square root of 108 by Prime FactorizationThe prime factorization method is one of the useful methods to find the square root of a number. Here we will find the square root of 108 by the prime factorization method. At first, we have to factorize the number 108. As 108 is an even number, it will be divisible by 2. So we have 108=2×54. Now we will factorize 54 and by the above logic, we get that 54=2×27. We know that 27=3×9 and 9=3×3. So finally we get that 108=2×2×3×3×3 …(∗) The above is the prime factorization of 108. Taking square root on both sides of (∗), we get that $\sqrt{108}=\sqrt{2 \times 2 \times 3 \times 3 \times 3}$ After making pairs of two equal numbers, we have $\sqrt{108}=\sqrt{2 \times 2} \times \sqrt{3 \times 3} \times \sqrt{3}$ $=2 \times 3 \times \sqrt{3}$ $[\because \sqrt{a \times a}=a]$ $=6\sqrt{3}$ ∴ the value of the square root of $108$ is $6\sqrt{3}.$ Question Answer on Root 108
Important Things of Root 108:
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