Square Root of 20

A number is said to be a square root of a certain number when it produces a quantity or a number when multiplied by itself. Square root for a number can be defined as the inverse operation of squaring a number. The symbol \[\sqrt {}\] is used for square roots and is always positive. For instance, the square root of 25 is 5, which can be simplified with the below diagram:

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Suppose X is a number, and the square root of X is "Y". Then, it is denoted as \[\sqrt{x}\] = Y  . The same can be written as X = Y².

When a positive number is multiplied by itself, it gives the square of the number as positive.

The square root of imperfect squares is tricky, and the answer is always in decimal numbers.

Finding the square root of perfect squares is quite an easy task (like for 4, 9, 16, 25, and so on) but finding square roots of imperfect squares is a tricky thing. Numbers 3.5, 7, 8, ..., 20, and so on are imperfect squares.

Methods for Finding the Square Root

There are four different methods of finding the square roots. They are given as follows:

1. Repeated subtraction method

2. Prime factorization method

3. Estimation method of the square root

4. Long division method of the square root

Mostly a, b, and c methods are used for convenience and for the numbers that are perfect squares. The d method is used for any number irrespective of it being a perfect square or not.

Finding Square Root of 20

Before proceeding with finding square roots, students must be aware of the difference between “a square of a number” and “square root of a number.”. For example, when a question asks square of 20, the answer is 20 x 20, that is 20² = 400, while the question says the square root of 20 has to be solved in the way mentioned below.

The square root of 20 is also known as under root of 20 or square root for 20 or radical of 20. The \[\sqrt {}\]   is said to be radical, and the number appearing beneath it is radicand. For \[\sqrt {20}\]  ,  20 is a radicand.

The value under root of 20 or root 20 value or  root of 20 is 4.472135955.

4.472135955 is the square root of 20 or value of under root 20 and is represented as \[\sqrt {20}\] in radical form. The \[\sqrt {20}\] in simplest form is written as \[2\sqrt{5}\].

Using a calculator and finding the answer is easy, but as a student, knowing the method of finding square root is a must.

This is possible by utilizing two methods: prime factorization and the long division method. Both methods are simple and are easy to find the square root.

Rounding off, square root of 20 or \[\sqrt{20}\] = 4.4721. \[\sqrt{20}\] is an irrational number since it can also be written as 25, where 5 is an irrational number.

Proceeding further to find the value of \[\sqrt{20}\].

I.  Prime Factorization Method to Find Square Root of 20

This is the easiest method to find the value of \[\sqrt{20}\]  or the value of under root \[\sqrt{20}\]  .

To simplify, let's understand what the prime factorization method is in short – iIt is breaking down the numbers into a multiplication product of prime numbers.

The prime factorization of 20 is 

20 = 2 x 2 x 5 .

In the above example, we can pair two identical prime numbers together and write them as 2², while 5 cannot be paired.

Hence, 2² can be written as 2, and 5 is written as √5.

Thus, \[\sqrt{20}\]= \[\sqrt{2 \times 2 \times \times 5}\]

Therefore, taking 2 outside the root ( as it can be paired together) while 5 can't, we get,

\[\sqrt{20}\]= \[2\sqrt{5}\]

Simplifying this little further, finding the square root of 5 from the square root table, we get \[\sqrt{5}\] = 2.236.

Hence, the  answer for \[\sqrt{20}\]=\[2\sqrt{5}\]

= 2 x 2.236

= 4.472.

 II.  Long Division Method for Finding the Square Root of 20

Well, we have learned to find the square root of 20 by the prime factorisation method. But to calculate the value of under root 20, it is important to know the value of 5. Even 5 is an imperfect square, and it becomes difficult to find the accurate value of 20 without a square root table.

Therefore, for imperfect squares, the long division method is used to find the value of square roots accurately.

The steps for finding the square root of 20 up to 6 decimal places, hence we have taken 20.000000. Put the bar over the paired numbers from the right-hand side:

1. Take the number whose square root has to be evaluated.

2. Pair the number from the unit place or the right-hand side of the number.

3. Take the number that is closer to the square of the number paired. Here 16 is closer to the number 20. Hence, the square root of 16, that is 4, should be taken as a divisor.

4. Dividing the number by 4, the quotient comes to 4, and the remainder is 4. Carry down the next pair of numbers "00". ( The number 20 is written as 20.00000.).

5. Now the quotient 4 should be doubled and written in the divisor place that is 8, and in the unit's place, write a number that comes closer or equal to 400. By the hit and trial method, 84 x 4 comes to 336, which is closer to 400.

6. The remainder is 64, and carrying down the "00", we derive 6400. Now again, double up the quotient (ignoring the decimal, it is 44); hence, the divisor will be 88, and in the unit's place, write a number that comes closer or equal to 6400. By hit and trial method, 887 x 7 = 6209.

7. The remainder is 191 and again, carrying down "00", it becomes 19100. In the quotient's place, the divisor will be (447 x 2 = 894). In the unit's place, write a number that comes closer or equal to 19100. Thus, the quotient 4.472 is the square root of 20.

8. If you want to find 2 square roots of 20, it comes to 4.472 x 2 = 8.944.

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Conclusion

Finding the square root of 20 is done by using two methods: Prime factorization and the long division method. Both methods are simple and are easy to find the square root.