Square Root of 48

Before we begin, let's understand the meaning of the square root. The symbol square root is written as √ and is an integral part of mathematics. Once you understand the basics of finding the square root of a number, you can solve any square root-related problem. In this short lesson, we will learn about the square root of 48 and find it with different methods like long division method. Let us see what the square root of 48 is.

• Square Root of 48: √48 = 6.928
• Square of 48: 48² = 2304

The square root of a number is the number that gets multiplied to itself to give the product. The square root of 48 is 6.92820323. Square root of 48 in the radical form is expressed as √48  and in exponent form, it is expressed as 48^1/2. The square root of 48 rounded to 5 decimal places is  6.9282...

Any number which cannot be expressed as p/q  where p and q are integers and q is not equal to 0 are irrational numbers. Can √48 express in such a way? Also in the decimal form, we see that the decimal part of √48 is 6.92820323028... which is non-terminating, non-repeating, and never-ending. Hence√48 is an irrational number.

48 is not a perfect square. We can find the square root of 48 by the approximation method. For the accurate value, we can use the long division method. In the approximation method, we find square numbers close to 48. We see that 36 and 49 are the perfect square numbers close to 48. The square root of 36 is 6 and the square root of 49 is 7. Therefore the square root of 48 must lie between 6 and 7 and more close to 7 as 48 is closer to 49. This method only gives us an approximate answer. To know the exact value we can use the long division method and find a more accurate decimal value for √48.

Simplified Radical Form of Square Root of 48

48 is a composite number. When we find square root of any number, we take one number from each pair of the same numbers from its prime factorization and we multiply them. 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.

Let us follow the steps to find the square root of 48 by long division.

• Step 1: Starting from the right, we will pair up the digits by putting a bar above them.
• Step 2: Find a number which, when multiplied to itself, gives the product less than or equal to 48. So, the number is 4. Putting the divisor as 6, we get the quotient as 6 and the remainder 36.
• Step 3: Now double the divisor. Guess the largest possible digit which will also become the new digit in the quotient, such that when the new divisor is multiplied to the new quotient the product is less than or equal to the dividend. Divide and write the remainder.

Explore Square roots using illustrations and interactive examples

• Square Root of 64
• Square Root of 36
• Square Root of 28
• Square Root of 25
• Square Root of 45

Important Notes:

• In exponent form square root of 48 is expressed as 48^1/2.
• The real roots of √48 are 6.928.

Challenging Questions:

• What is the value of √√48?
• Determine the square root of -48.

What is the square root of 48?

The square root of 48 is 6.92820323.

Can we find the square root of 48 by the approximation method?

Yes, we can estimate the square root of 48 using the approximation method. This method can only be used if the given number lies between two consecutive perfect squares.

How do you find the square root of 48?

We can find the square root of 48 by using the prime factorization, repeated subtraction, and long division.

Is the square root of 48 an irrational number?

Yes, the square root of 48 is an irrational number.

What is the square root of 48 in simplified form?

The square root of 48 in simplified form is 4√3.