The square root of 20 is written as √20, which √ is the radical sign and 20 is referred to as the radicand. The number 20 can be expressed as 25 in its most basic form.
As a result, we cannot conclude that 20 is a rational number because 5 is an irrational number.
Let us now study how to find the value of 20.
20 square root | Square Root of 20
The prime factorization method is used to calculate the square root for 20.
Prime factorization of 20
Factorizing the integer under the root, or 20 as it is known, is the simplest way to discover the value of √20.
The result of 20’s prime factorization is
20 = 2 x 2 x 5 = 22 x 5
As a result, we can observe that 20 is not a perfect square since, after factoring 20, we are unable to couple the fifth number. Out of the root, only 22 can be removed.
Consequently, if we combine the roots from both sides, we have;
√20 = √ (2 x 2 x 5)
We only have one set of numbers in this situation, which is 2. Consequently, when we remove it from the root, we have;
√20 = 2√5
We know the value of √5 = 2.236 from the square root table.
√20 = 2 x 2.236
√20 = 4.472
Using Long Division Method
We learned how to use prime factorization to compute the value of the square root of 20. However, it is not a direct technique because 20 is an imperfect square and we must recall the √5 value to obtain the precise value of √20.
We may use the precise value of √20 by utilizing the long division approach. The solution step to evaluate 20 is shown below.