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Square Root of 490

The square root of 490 is expressed as √490 in the radical form and as (490)^½ or (490)^0.5 in the exponent form. The square root of 490 rounded up to 9 decimal places is 22.135943621. It is the positive solution of the equation x² = 490. We can express the square root of 490 in its lowest radical form as 7 √10.

Square Root of 490: 22.135943621178654
Square Root of 490 in exponential form: (490)^½ or (490)^0.5
Square Root of 490 in radical form: √490 or 7 √10

Square Root of 490

1.	What is the Square Root of 490?
2.	How to find the Square Root of 490?
3.	Is the Square Root of 490 Irrational?
4.	FAQs

What is the Square Root of 490?

The square root of 490, (or root 490), is the number which when multiplied by itself gives the product as 490. Therefore, the square root of 490 = √490 = 7 √10 = 22.135943621178654.

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How to Find Square Root of 490?

Square Root of 490 by Long Division Method

Value of √490 by Long Division Method

Explanation:

Forming pairs: 04 and 90
Find a number Y (2) such that whose square is <= 4. Now divide 04 by 2 with quotient as 2.
Bring down the next pair 90, to the right of the remainder 0. The new dividend is now 90.
Add the last digit of the quotient (2) to the divisor (2) i.e. 2 + 2 = 4. To the right of 4, find a digit Z (which is 2) such that 4Z × Z <= 90. After finding Z, together 4 and Z (2) form a new divisor 42 for the new dividend 90.
Divide 90 by 42 with the quotient as 2, giving the remainder = 90 - 42 × 2 = 90 - 84 = 6.
Now, let's find the decimal places after the quotient 22.
Bring down 00 to the right of this remainder 6. The new dividend is now 600.
Add the last digit of quotient to divisor i.e. 2 + 42 = 44. To the right of 44, find a digit Z (which is 1) such that 44Z × Z <= 600. Together they form a new divisor (441) for the new dividend (600).
Divide 600 by 441 with the quotient as 1, giving the remainder = 600 - 441 × 1 = 600 - 441 = 159.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 490.

Therefore, the square root of 490 by long division method is 22.1 approximately.

Is Square Root of 490 Irrational?

The actual value of √490 is undetermined. The value of √490 up to 25 decimal places is 22.13594362117865532399225. Hence, the square root of 490 is an irrational number.

☛ Also Check:

Square Root of 36 - √36 = 6
Square Root of 96 - √96 = 9.79796
Square Root of 113 - √113 = 10.63015
Square Root of 400 - √400 = 20
Square Root of 73 - √73 = 8.54400
Square Root of 12 - √12 = 3.46410
Square Root of 289 - √289 = 17

Square Root of 490 Solved Examples

Example 1: Solve the equation x² − 490 = 0

Solution:

x² - 490 = 0 i.e. x² = 490
x = ±√490
Since the value of the square root of 490 is 22.136,
⇒ x = +√490 or -√490 = 22.136 or -22.136.
Example 2: If the area of a square is 490 in². Find the length of the side of the square.

Solution:

Let 'a' be the length of the side of the square.
⇒ Area of the square = a² = 490 in²
⇒ a = ±√490 in
Since length can't be negative,
⇒ a = √490 = 22.136 in
Example 3: If the area of an equilateral triangle is 490√3 in². Find the length of one of the sides of the triangle.

Solution:

Let 'a' be the length of one of the sides of the equilateral triangle.
⇒ Area of the equilateral triangle = (√3/4)a² = 490√3 in²
⇒ a = ±√1960 in
Since length can't be negative,
⇒ a = √1960 = 2 √490
We know that the square root of 490 is 22.136.
⇒ a = 44.272 in

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FAQs on the Square Root of 490

What is the Value of the Square Root of 490?

The square root of 490 is 22.13594.

Why is the Square Root of 490 an Irrational Number?

Upon prime factorizing 490 i.e. 2¹ × 5¹ × 7², 2 is in odd power. Therefore, the square root of 490 is irrational.

What is the Square Root of 490 in Simplest Radical Form?

We need to express 490 as the product of its prime factors i.e. 490 = 2 × 5 × 7 × 7. Therefore, √490 = √2 × 5 × 7 × 7 = 7 √10. Thus, the square root of 490 in the lowest radical form is 7 √10.

What is the Square Root of -490?

The square root of -490 is an imaginary number. It can be written as √-490 = √-1 × √490 = i √490 = 22.135i
where i = √-1 and it is called the imaginary unit.

What is the Value of 19 square root 490?

The square root of 490 is 22.136. Therefore, 19 √490 = 19 × 22.136 = 420.583.

What is the Square of the Square Root of 490?

The square of the square root of 490 is the number 490 itself i.e. (√490)² = (490)^2/2 = 490.

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