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How to Solve under Root Without Calculator

To solve an under-root problem without a calculator, start by writing down the equation. Then, estimate what the answer is likely to be and use it as your starting point. Next, divide both sides of the equation by the number before the under-root symbol.

This will result in a new equation with one root on each side. Simplify this equation until you have isolated the variable inside of one root sign on one side of the equal sign. Finally, plug in different values for that variable until you find an answer that equals both sides of your original equation.

Repeat this process if needed to get closer to your desired answer.

  • Step 1: Recognize the type of equation
  • If there is an even root, first use a substitution to make it into a square root
  • For example, if you have √64, substitute x² = 64 and solve for x using basic algebra (x = ± 8)
  • Step 2: Simplify the expression under the root sign as much as possible by factoring out perfect squares or any common factors that can be found within the terms inside of the radical symbol
  • Step 3: Estimate what number multiplied with itself will equal or be close to this simplified value from Step 2
  • This process may involve trial and error several times in order to find an accurate result
  • Step 4: Use your estimate from Step 3 along with other calculations such as adding/subtracting fractions or decimals, multiplication and division to obtain your final answer
How to Solve under Root Without Calculator


How Do You Find the Roots Without a Calculator?

Finding the roots of an equation without a calculator can be challenging, but it is possible. The easiest way to do this is by using factoring and the quadratic formula. First, use factoring to see if you can find the two factors that add up to the coefficient of x squared in your equation.

If you are able to factor out a perfect square (e.g., 4x^2 – 16 = 0), then you already have one root – any number multiplied by itself will equal zero when squared (in our example, 4 * -4 = 16). On other equations with more complex coefficients (e.g., 2x^2 + 7x – 12 = 0), you may need to use trial-and-error or guesswork until you find two numbers whose product equals your coefficient and whose sum equals your constant term on the right side of your equation (in our example, 3 * -4 = -12 and 3 + (-4) = -1). After finding these two numbers, simply plug them into the quadratic formula: x=(-(b)+/-sqrt((b)^2-(4*a*c))/2a where b is equal to whichever number was not used as part of ourFactored result from earlier and c is equal to whatever number was used in our Factored solution from earlier.

. This should give us both roots for our equation!

How Do You Manually Calculate under Root?

To manually calculate the square root of a number, first divide it into two parts – its integral part and fractional part. Once that is done, you can start breaking down the integral part of your number by separating out pairs from right to left, starting with the largest pair possible. Next, add up these pairs in order to determine what multiple of two will give you this total.

This multiple should be written directly above the original pair. Now take a guess at which multiple would result in your original number when multiplied by itself i.e., your square root guess and then subtract this product from your original number. The remainder obtained after subtracting becomes the new dividend which is used for further calculations until you find an exact answer or until you come close enough to a perfect square root value; usually within around five decimal places accuracy is considered good enough when doing manual calculations like these!

How Do You Calculate under Root?

Calculating the square root of a number is simple with today’s technology, but it can also be done using manual methods if you know how. To calculate the square root of any number, start by finding two perfect squares that are closest to your target number and then subtract them from your target number. For example, to find the square root of 25, take 16 (4×4) away from 25 which leaves 9.

Then take 3 (3×3) away from 9 which leaves 6. The remaining difference between your original number and these two perfect squares is what you need to work out in order to get your answer: 6 = 2 x 3 = √25.

How Do You Simplify Square Roots Without a Calculator?

Simplifying square roots without a calculator can be tricky but it is possible. To start, determine if the number under the root sign is perfect. If it is, then you already have your answer; for example the square root of 4 would simply be 2.

If not, factor the number into two or more numbers that when multiplied together equal each other and use those factors as part of your answer; for instance, √18 could be simplified to 3√2 since 18 = (3)(6) and √(3)(6) = 3√2. You can also use prime factorization to simplify square roots by breaking down a larger number into its smallest components and using them in your equation; for example 24 could be broken down into (2)(2)(2)(3). The square root of 24 would then become 2√(2)(3), which simplifies to 2√6 or simply 6.

With practice this method becomes easier and eventually you will find yourself able to simplify any given square root quickly without needing a calculator at all!

How to Calculate Square Root Without Calculator

How to Find Square Root Manually

Finding the square root of a number can be done manually by using the long division method. To begin, divide the number into pairs of two digits starting from right to left and write them down below in groups of two. Then, find the largest perfect square that is less than or equal to each pair and subtract it from its corresponding pair.

Write down this difference as well as the divisor (the answer found when subtracting) at its side. Finally, continue doing this same process until you reach your desired result!

How to Find Square Root Without Calculator Khan Academy

If you would like to learn how to find a square root without using a calculator, Khan Academy is a great resource. They offer tutorials and lessons on the subject that will help you understand the basic concepts of finding square roots and other related math topics. The tutorial videos are easy to follow along with as well so if you’re feeling stuck at any point, just start from the beginning again!

How to Find Square Root Without Calculator Using Prime Factorization

Finding the square root of a number without using a calculator can be done using prime factorization. This involves breaking down the number into its prime factors and then taking out any squared numbers until you get to the desired square root. For example, if you wanted to find the square root of 25, it would first need to be broken down into 5 x 5 = 25.

How to Calculate Square Root by Division Method

The Division Method is a simple and effective way to calculate the square root of any number. To use this method, you will need to divide your chosen number by two until you get a result that can be divided one more time without a remainder. After each division, write down the quotient as well as the divisor used in order to keep track of progress.

Once you reach a point where no further divisions are possible, you have found the square root of your original number!


In conclusion, solving equations with square roots can be daunting without a calculator. However, it is possible to solve these equations using the methods described in this blog post. The steps involve first separating the equation into two factors and then finding out which numbers combine to create the number under the root sign when multiplied together.

Lastly, you have to determine if both factors are positive or negative so that you can accurately express your solution. With practice and dedication, anyone should be able to quickly and effectively solve any equation with a square root without requiring a calculator!