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Square Root of 257

The square root of 257 is expressed as √257 in the radical form and as (257)^½ or (257)^0.5 in the exponent form. The square root of 257 rounded up to 5 decimal places is 16.03122. It is the positive solution of the equation x² = 257.

Square Root of 257: 16.0312195418814
Square Root of 257 in exponential form: (257)^½ or (257)^0.5
Square Root of 257 in radical form: √257

Square Root of 257

1.	What is the Square Root of 257?
2.	How to find the Square Root of 257?
3.	Is the Square Root of 257 Irrational?
4.	FAQs

What is the Square Root of 257?

The square root of 257, (or root 257), is the number which when multiplied by itself gives the product as 257. Therefore, the square root of 257 = √257 = 16.0312195418814.

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How to Find Square Root of 257?

Square Root of 257 by Long Division Method

Value of √257 by Long Division Method

Explanation:

Forming pairs: 02 and 57
Find a number Y (1) such that whose square is <= 2. Now divide 02 by 1 with quotient as 1.
Bring down the next pair 57, to the right of the remainder 1. The new dividend is now 157.
Add the last digit of the quotient (1) to the divisor (1) i.e. 1 + 1 = 2. To the right of 2, find a digit Z (which is 6) such that 2Z × Z <= 157. After finding Z, together 2 and Z (6) form a new divisor 26 for the new dividend 157.
Divide 157 by 26 with the quotient as 6, giving the remainder = 157 - 26 × 6 = 157 - 156 = 1.
Now, let's find the decimal places after the quotient 16.
Bring down 00 to the right of this remainder 1. The new dividend is now 100.
Add the last digit of quotient to divisor i.e. 6 + 26 = 32. To the right of 32, find a digit Z (which is 0) such that 32Z × Z <= 100. Together they form a new divisor (320) for the new dividend (100).
Divide 100 by 320 with the quotient as 0, giving the remainder = 100 - 320 × 0 = 100 - 0 = 100.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 257.

Therefore, the square root of 257 by long division method is 16.0 approx.

Is Square Root of 257 Irrational?

The actual value of √257 is undetermined. The value of √257 up to 25 decimal places is 16.03121954188139736487135. Hence, the square root of 257 is an irrational number.

☛ Also Check:

Square Root of 120 - √120 = 10.95445
Square Root of 25 - √25 = 5
Square Root of 125 - √125 = 11.18034
Square Root of 54 - √54 = 7.34847
Square Root of 76 - √76 = 8.71780
Square Root of 625 - √625 = 25
Square Root of 90 - √90 = 9.48683

Square Root of 257 Solved Examples

Example 1: Solve the equation x² − 257 = 0

Solution:

x² - 257 = 0 i.e. x² = 257
x = ±√257
Since the value of the square root of 257 is 16.031,
⇒ x = +√257 or -√257 = 16.031 or -16.031.
Example 2: If the surface area of a cube is 1542 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 = 1542 in²
⇒ a = ±√257 in
Since length can't be negative,
⇒ a = √257
We know that the square root of 257 is 16.031.
⇒ a = 16.031 in
Example 3: If the area of a circle is 257π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 257π in²
⇒ r = ±√257 in
Since radius can't be negative,
⇒ r = √257
The square root of 257 is 16.031.
⇒ r = 16.031 in

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FAQs on the Square Root of 257

What is the Value of the Square Root of 257?

The square root of 257 is 16.03121.

Why is the Square Root of 257 an Irrational Number?

The number 257 is prime. This implies that the number 257 is pairless and is not in the power of 2. Therefore, the square root of 257 is irrational.

Evaluate 2 plus 20 square root 257

The given expression is 2 + 20 √257. We know that the square root of 257 is 16.031. Therefore, 2 + 20 √257 = 2 + 20 × 16.031 = 2 + 320.624 = 322.624

Is the number 257 a Perfect Square?

The number 257 is prime. This implies that the square root of 257 cannot be expressed as a product of two equal integers. Therefore, the number 257 is not a perfect square.

What is the Value of 9 square root 257?

The square root of 257 is 16.031. Therefore, 9 √257 = 9 × 16.031 = 144.281.

If the Square Root of 257 is 16.031. Find the Value of the Square Root of 2.57.

Let us represent √2.57 in p/q form i.e. √(257/100) = 2.57/10 = 1.603. Hence, the value of √2.57 = 1.603

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