The square root of 49 is a number when multiplied by itself will be 49. If a square has an area of 49 unit^{2}, 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**.

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**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**is the exponential form of square root of^{1/2}**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=7^{2}

Taking square root on both sides, we have

√49 = √7^{2}

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

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

= 7^{1 }= 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 the area 49 unit
^{2}

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