Square root of 20 – Value, Derivation and Examples

The square root of 20 value

The square root of a number is the value that, when multiplied by itself, gives the original value. It is the inverse of squares. Root 20 is denoted as √20 in its radical form. Its square root, rounded up to three decimal spaces, is 4.472. The value of √20 can also be negative, that is -4.472. But in this article we will be considering only its positive value.

Is root 20 an irrational number?

The value of root 20 is an irrational number because the decimal form of √20 is non terminating, and at the same time, it is non-recurring. That means none of its digits in the decimal space ever repeat themselves, nor can we see a pattern in their appearance. 

Now, we’re going to look at the methods of finding out the value of √20.

Finding the value of √20 using the long division method:-

The long division method is one of the most convenient ways of determining the root values of numbers. Here, we’ll follow these steps to find the value of root 20 by long division method:-

Step 1:

Make a pair of digits (by placing a bar over it) from the unit’s place.

Step 2:

We’ll now have to find a number such that when it is multiplied by itself, the product is less than or equal to 20.

We know that 4² gives us 16, and 16 is less than 20. So it becomes our divisor. 

Step 3:

Next, we’ll place a decimal point and a pair of zeros next to it and continue our division. Now, we multiply the quotient by 2, and the product becomes the starting digit of our next divisor.

Step 4:

Now we’ll have to choose a number in the unit’s place for the new divisor such that its product with a number is less than or equal to 400.

So, the closest multiplication we’re left with is 84 × 4 = 336

Step 5:

We bring down the next pair of zeros and add 4 to the quotient, and we get the starting digit of the new divisor.

Step 6:

Now, we choose a number in the unit’s place for the new divisor such that its product with a number is less than or equal to 6400. 6209 is the nearest number possible, leaving us with a remainder of 191.

Step 7:

More pairs of zeros are added, and the process is repeated to find the new divisor and product as in step 2.

Simplification of root 20

If you think that long division is time-consuming, you can find the value of √20 by simplification. But, first, you must find the prime factors of 20. 

20 = 2 x 2 x 5

Now, we can see that we cannot pair the number 5. Therefore, 20 is a non-perfect square. Adding root on both sides.

We get, √20 = √(2 x 2 x 5)

Now, since we can make a pair of the number 2, we can take it out from the root but leave the number 5 within the root. 

√20 = √(2 x 2 x 5)

√20 = 2√5

√20 = 2 x 2.236 because √5 = 2.236

So, √20 = 4.472

Solved Question

Question 1: Find the value of ‘x’ if x² = 20
Solution: Given, x² = 20
x = √20
x = √(2 x 2 x 5)
x = √(4 x 5)
we know that √4 = 2
so, x = 2 (√5)
x = 2 x 2.236
x = 4.472

Question 2: Calculate the length of the diagonal of a square sheet if its sides are √20cm each. 
Solution: Side ‘s’ of the square sheet = √20cm
By applying Pythagoras theorem, the diagonal of square = √2 x s 
= √2 x √20
= 1.732 x 4.472 cm
= 7.74 cm
Therefore, the diagonal of the square sheet is 7.74 cm.