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Square Root of 217

The square root of 217 is expressed as √217 in the radical form and as (217)^½ or (217)^0.5 in the exponent form. The square root of 217 rounded up to 5 decimal places is 14.73092. It is the positive solution of the equation x² = 217.

Square Root of 217: 14.730919862656235
Square Root of 217 in exponential form: (217)^½ or (217)^0.5
Square Root of 217 in radical form: √217

Square Root of 217

1.	What is the Square Root of 217?
2.	How to find the Square Root of 217?
3.	Is the Square Root of 217 Irrational?
4.	FAQs

What is the Square Root of 217?

The square root of 217, (or root 217), is the number which when multiplied by itself gives the product as 217. Therefore, the square root of 217 = √217 = 14.730919862656235.

☛ Check: Square Root Calculator

How to Find Square Root of 217?

Square Root of 217 by Long Division Method

Value of √217 by Long Division Method

Explanation:

Forming pairs: 02 and 17
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 17, to the right of the remainder 1. The new dividend is now 117.
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 4) such that 2Z × Z <= 117. After finding Z, together 2 and Z (4) form a new divisor 24 for the new dividend 117.
Divide 117 by 24 with the quotient as 4, giving the remainder = 117 - 24 × 4 = 117 - 96 = 21.
Now, let's find the decimal places after the quotient 14.
Bring down 00 to the right of this remainder 21. The new dividend is now 2100.
Add the last digit of quotient to divisor i.e. 4 + 24 = 28. To the right of 28, find a digit Z (which is 7) such that 28Z × Z <= 2100. Together they form a new divisor (287) for the new dividend (2100).
Divide 2100 by 287 with the quotient as 7, giving the remainder = 2100 - 287 × 7 = 2100 - 2009 = 91.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 217.

Therefore, the square root of 217 by long division method is 14.7 approximately.

Is Square Root of 217 Irrational?

The actual value of √217 is undetermined. The value of √217 up to 25 decimal places is 14.73091986265623535857537. Hence, the square root of 217 is an irrational number.

☛ Also Check:

Square Root of 106 - √106 = 10.29563
Square Root of 288 - √288 = 16.97056
Square Root of 15 - √15 = 3.87298
Square Root of 19 - √19 = 4.35890
Square Root of 120 - √120 = 10.95445
Square Root of 125 - √125 = 11.18034
Square Root of 2 - √2 = 1.41421

Square Root of 217 Solved Examples

Example 1: Solve the equation x² − 217 = 0

Solution:

x² - 217 = 0 i.e. x² = 217
x = ±√217
Since the value of the square root of 217 is 14.731,
⇒ x = +√217 or -√217 = 14.731 or -14.731.
Example 2: If the surface area of a cube is 1302 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 = 1302 in²
⇒ a = ±√217 in
Since length can't be negative,
⇒ a = √217
We know that the square root of 217 is 14.731.
⇒ a = 14.731 in
Example 3: If the area of a square is 217 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 = 217 in²
⇒ a = ±√217 in
Since length can't be negative,
⇒ a = √217 = 14.731 in

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FAQs on the Square Root of 217

What is the Value of the Square Root of 217?

The square root of 217 is 14.73091.

Why is the Square Root of 217 an Irrational Number?

Upon prime factorizing 217 i.e. 7¹ × 31¹, 7 is in odd power. Therefore, the square root of 217 is irrational.

Is the number 217 a Perfect Square?

The prime factorization of 217 = 7¹ × 31¹. Here, the prime factor 7 is not in the pair. Therefore, 217 is not a perfect square.

If the Square Root of 217 is 14.731. Find the Value of the Square Root of 2.17.

Let us represent √2.17 in p/q form i.e. √(217/100) = 2.17/10 = 1.473. Hence, the value of √2.17 = 1.473

What is the Square Root of -217?

The square root of -217 is an imaginary number. It can be written as √-217 = √-1 × √217 = i √217 = 14.73i
where i = √-1 and it is called the imaginary unit.

What is the Square of the Square Root of 217?

The square of the square root of 217 is the number 217 itself i.e. (√217)² = (217)^2/2 = 217.

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