Square root of 49: Rational? Perfect Square?

The square root of 49 is a number when multiplied by itself will be 49. If a square has an area of 49 unit², then we use the value of the square root of 49 to find the length of the square. The square root of 49 is denoted by the symbol √49. In this section, we will learn how to find the value of √49.

The value of the square root of 49 is 7.

Important Things about Square Root of 49:

• √49 = 7
• 49 is a perfect square.
• √49 is the radical form of square root of 49.
• 49^1/2 is the exponential form of square root of 49.
• The square root of 49 is 7.000 in decimal form.
• Square of 49: 49×49 = 2401

Let us now calculate the square root of 49.

What is the Square Root of 49?

Note that the value of the square root of 49 is 7. To prove this, we will write 49 as a square of some numbers as 49 is a perfect square.

Observe that 49 is a product of two numbers of 7‘s. So we write

49=7×7=7²

Taking square root on both sides, we have

√49 = √7²

As square root can be written as power 1/2, we get that

√49 = (7²)^1/2 = 7^2×1/2   as we know that (a^m)ⁿ = a^m×n

= 7¹ = 7

So the square root of 49 is 7.

 

Is 49 a perfect square number?

We have calculated above that √49=7. As the number 7 is a whole number, we get that the square root of 49 is also a whole number.

So by the definition of a perfect square, we conclude that 49 is a perfect square number.

 

Square root of 49 by Prime Factorization

We will now find the square root of 49 by the prime factorization method. At first, we have to factorize 49. See that 49 is divisible by the prime number 7 only.

So we have

49=7×7. 

Taking square root on both sides, we get that

√49 = √(7×7)

= 7 as we know that √a×a=a 

∴  the square root of 49 is 7. 

Is Square Root of 49 Rational?

By definition, a rational number can be expressed as p/q where p and q are integers with q ≠ 0.

We have obtained that √49=7.

Note that 7=7/1. So 7 can be written as p/q with p=7, q=1≠0.

∴ 7 is a rational number.

Hence the square root of 49 is also a rational number.

Conclusion: √49 is not an irrational number.

 

Key Things about 49

• 49 is a composite odd number.
• A square of length 7 unit has an area 49 unit²

If you want to know more about square roots, visit the following pages:

• Basic concepts of square roots
• Properties of square roots

Question Answer on Square Root of 49

No.	Question	Answer
1	Is the square root of 49 a whole number?	As √49 = 7 is a whole number, it follows that root 49 is a whole number.
2	Is the square root of 49 irrational?	Root 49 is not an irrational number, as √49 = 7.
3	Is the square root of 49 rational?	Yes, square root of 49 is a rational number.
4	Is the square root of 49 a natural number?	Yes, square root of 49 is a natural number as √49 = 7 is so.
5	Is √49 rational or irrational?	√49 is rational.
6	Is 49 a perfect square root?	As 7×7=49, the number 49 is a perfect square.