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Square Root of 4900

The square root of 4900 is expressed as √4900 in the radical form and as (4900)^½ or (4900)^0.5 in the exponent form. The square root of 4900 is 70. It is the positive solution of the equation x² = 4900. The number 4900 is a perfect square.

Square Root of 4900: 70
Square Root of 4900 in exponential form: (4900)^½ or (4900)^0.5
Square Root of 4900 in radical form: √4900

Square Root of 4900

1.	What is the Square Root of 4900?
2.	How to find the Square Root of 4900?
3.	Is the Square Root of 4900 Rational?
4.	FAQs

What is the Square Root of 4900?

The square root of 4900, (or root 4900), is the number which when multiplied by itself gives the product as 4900. Therefore, the square root of 4900 = √4900 = 70.

☛ Check: Square Root Calculator

How to Find Square Root of 4900?

Square Root of 4900 by Long Division Method

Value of √4900 by Long Division Method

Explanation:

Forming pairs: 49 and 00
Find a number Y (7) such that whose square is <= 49. Now divide 49 by 7 with quotient as 7.
Bring down the next pair 00, to the right of the remainder 0. The new dividend is now 0.
Add the last digit of the quotient (7) to the divisor (7) i.e. 7 + 7 = 14. To the right of 14, find a digit Z (which is 0) such that 14Z × Z <= 0. After finding Z, together 14 and Z (0) form a new divisor 140 for the new dividend 0.
Divide 0 by 140 with the quotient as 0, giving the remainder = 0 - 140 × 0 = 0 - 0 = 0.
We stop the process since the remainder is now 0 and there are no more digits that can be brought down.

Therefore, the square root of 4900 by long division method is 70.

Is Square Root of 4900 Rational?

The value of √4900 is 70. Hence, the square root of 4900 is a rational number.

☛ Also Check:

Square Root of 63 - √63 = 7.93725
Square Root of 108 - √108 = 10.39230
Square Root of 68 - √68 = 8.24621
Square Root of 65 - √65 = 8.06226
Square Root of 44 - √44 = 6.63325
Square Root of 60 - √60 = 7.74597
Square Root of 39 - √39 = 6.24500

Square Root of 4900 Solved Examples

Example 1: Solve the equation x² − 4900 = 0

Solution:

x² - 4900 = 0 i.e. x² = 4900
x = ±√4900
Since the value of the square root of 4900 is 70,
⇒ x = +√4900 or -√4900 = 70 or -70.
Example 2: If the surface area of a sphere is 19600π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 19600π in²
⇒ r = ±√4900 in
Since radius can't be negative,
⇒ r = √4900
The square root of 4900 is 70.
⇒ r = 70 in
Example 3: If the surface area of a cube is 29400 in². Find the length of the side of the cube.

Solution:

Let 'a' be the length of the side of the cube.
⇒ Area of the cube = 6a² = 29400 in²
⇒ a = ±√4900 in
Since length can't be negative,
⇒ a = √4900
We know that the square root of 4900 is 70.
⇒ a = 70 in

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FAQs on the Square Root of 4900

What is the Value of the Square Root of 4900?

The square root of 4900 is 70.

Why is the Square Root of 4900 a Rational Number?

Upon prime factorizing 4900 i.e. 2² × 5² × 7², we find that all the prime factors are in even power. This implies that the square root of 4900 is a positive integer. Therefore, the square root of 4900 is rational.

Evaluate 12 plus 12 square root 4900

The given expression is 12 + 12 √4900. We know that the square root of 4900 is 70. Therefore, 12 + 12 √4900 = 12 + 12 × 70 = 12 + 840 = 852

What is the Value of 1 square root 4900?

The square root of 4900 is 70. Therefore, 1 √4900 = 1 × 70 = 70.

Is the number 4900 a Perfect Square?

The prime factorization of 4900 = 2² × 5² × 7². Here, all the numbers are in the power of 2. This implies that the square root of 4900 is a positive integer. Therefore, 4900 is a perfect square.

If the Square Root of 4900 is 70. Find the Value of the Square Root of 49.

Let us represent √49 in p/q form i.e. √(4900/100) = 49/10 = 7. Hence, the value of √49 = 7

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