Square root of 48 in radical form

Here we will show you two methods that you can use to simplify the square root of 48. In other words, we will show you how to find the square root of 48 in its simplest radical form using two different methods.

To be more specific, we have created an illustration below showing what we want to calculate. Our goal is to make "A" outside the radical (√) as large as possible, and "B" inside the radical (√) as small as possible.

√48 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 48 to simplify the square root of 48. This is how to calculate A and B using this method:

A = Calculate the square root of the greatest perfect square from the list of all factors of 48. The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 48 divided by the greatest perfect square from the list of all factors of 48. We determined above that the greatest perfect square from the list of all factors of 48 is 16. Furthermore, 48 divided by 16 is 3, therefore B equals 3.

Now we have A and B and can get our answer to 48 in its simplest radical form as follows:

√48 = A√B

√48 = 4√3

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 48 to simplify the square root of 48 to its simplest form possible. This is how to calculate A and B using this method:

A = Multiply all the double prime factors (pairs) of 48 and then take the square root of that product. The prime factors that multiply together to make 48 are 2 x 2 x 2 x 2 x 3. When we strip out the pairs only, we get 2 x 2 x 2 x 2 = 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Divide 48 by the number (A) squared. 4 squared is 16 and 48 divided by 16 is 3. Therefore, B equals 3.

Once again we have A and B and can get our answer to 48 in its simplest radical form as follows:

√48 = A√B

√48 = 4√3

Simplify Square Root
Please enter another square root in the box below for us to simplify.

Simplify Square Root of 49
Here is the next square root on our list that we have simplifed for you.

Explanation:

To simplify #sqrt48#, we should first factorize #48#. As #2# is one factor, dividing 48 by 2, we get 24, which has factors 2 again. This way we go on till we get all the factors.

Hence #sqrt48=sqrt(2xx2xx2xx2xx3)#.

As #2# has appeared four times, square root of #2xx2xx2xx2# will be just #2xx2#. Note we cannot take square root of #3# as it has not appeared in pair.

Hence, #sqrt48=2xx2xxsqrt3# or #4sqrt3#

Here we will show you step-by-step how to simplify the square root of 48. The square root of 48 can be written as follows:

The √ symbol is called the radical sign. To simplify the square root of 48 means to get the simplest radical form of √48.

Step 1: List Factors
List the factors of 48 like so:

1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Step 2: Find Perfect Squares
Identify the perfect squares* from the list of factors above:

1, 4, 16

Step 3: Divide
Divide 48 by the largest perfect square you found in the previous step:

48 / 16 = 3

Step 4: Calculate
Calculate the square root of the largest perfect square:

√16 = 4

Step 5: Get Answer
Put Steps 3 and 4 together to get the square root of 48 in its simplest form:

Simplify Square Root Calculator
Please enter another Square Root for us to simplify:

Decimal Form
Square Root of 48 in Decimal form rounded to nearest 5 decimals:

6.9282

Exponent Form
Square Root of 48 written with Exponent instead of Radical:

48½ = 4 x 3½

Simplify Square Root of 49
The answer to Simplify Square Root of 48 is not the only problem we solved. Go here for the next problem on our list.

List of Perfect Squares

How do you simplify radical 48?

Simplified Radical Form of Square Root of 48 The factorization of 48 is 2 × 3 × 2 × 2 × 2 which has 1 pair of the same number. It can also be written as 48 = 2⁴ × 3¹. Thus, the simplest radical form of √48 is 4√3 itself.