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Square Root of 290

The square root of 290 is expressed as √290 in the radical form and as (290)^½ or (290)^0.5 in the exponent form. The square root of 290 rounded up to 5 decimal places is 17.02939. It is the positive solution of the equation x² = 290.

Square Root of 290: 17.029386365926403
Square Root of 290 in exponential form: (290)^½ or (290)^0.5
Square Root of 290 in radical form: √290

Square Root of 290

1.	What is the Square Root of 290?
2.	How to find the Square Root of 290?
3.	Is the Square Root of 290 Irrational?
4.	FAQs

What is the Square Root of 290?

The square root of 290, (or root 290), is the number which when multiplied by itself gives the product as 290. Therefore, the square root of 290 = √290 = 17.029386365926403.

☛ Check: Square Root Calculator

How to Find Square Root of 290?

Square Root of 290 by Long Division Method

Value of √290 by Long Division Method

Explanation:

Forming pairs: 02 and 90
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 90, to the right of the remainder 1. The new dividend is now 190.
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 7) such that 2Z × Z <= 190. After finding Z, together 2 and Z (7) form a new divisor 27 for the new dividend 190.
Divide 190 by 27 with the quotient as 7, giving the remainder = 190 - 27 × 7 = 190 - 189 = 1.
Now, let's find the decimal places after the quotient 17.
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. 7 + 27 = 34. To the right of 34, find a digit Z (which is 0) such that 34Z × Z <= 100. Together they form a new divisor (340) for the new dividend (100).
Divide 100 by 340 with the quotient as 0, giving the remainder = 100 - 340 × 0 = 100 - 0 = 100.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 290.

Therefore, the square root of 290 by long division method is 17.0 approximately.

Is Square Root of 290 Irrational?

The actual value of √290 is undetermined. The value of √290 up to 25 decimal places is 17.02938636592640116613332. Hence, the square root of 290 is an irrational number.

☛ Also Check:

Square Root of 72 - √72 = 8.48528
Square Root of 361 - √361 = 19
Square Root of 48 - √48 = 6.92820
Square Root of 41 - √41 = 6.40312
Square Root of 12 - √12 = 3.46410
Square Root of 36 - √36 = 6
Square Root of 1000 - √1000 = 31.62278

Square Root of 290 Solved Examples

Example 1: Solve the equation x² − 290 = 0

Solution:

x² - 290 = 0 i.e. x² = 290
x = ±√290
Since the value of the square root of 290 is 17.029,
⇒ x = +√290 or -√290 = 17.029 or -17.029.
Example 2: If the area of a circle is 290π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 290π in²
⇒ r = ±√290 in
Since radius can't be negative,
⇒ r = √290
The square root of 290 is 17.029.
⇒ r = 17.029 in
Example 3: If the area of an equilateral triangle is 290√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 = 290√3 in²
⇒ a = ±√1160 in
Since length can't be negative,
⇒ a = √1160 = 2 √290
We know that the square root of 290 is 17.029.
⇒ a = 34.059 in

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FAQs on the Square Root of 290

What is the Value of the Square Root of 290?

The square root of 290 is 17.02938.

Why is the Square Root of 290 an Irrational Number?

Upon prime factorizing 290 i.e. 2¹ × 5¹ × 29¹, 2 is in odd power. Therefore, the square root of 290 is irrational.

Is the number 290 a Perfect Square?

The prime factorization of 290 = 2¹ × 5¹ × 29¹. Here, the prime factor 2 is not in the pair. Therefore, 290 is not a perfect square.

What is the Square of the Square Root of 290?

The square of the square root of 290 is the number 290 itself i.e. (√290)² = (290)^2/2 = 290.

What is the Value of 15 square root 290?

The square root of 290 is 17.029. Therefore, 15 √290 = 15 × 17.029 = 255.441.

Evaluate 15 plus 16 square root 290

The given expression is 15 + 16 √290. We know that the square root of 290 is 17.029. Therefore, 15 + 16 √290 = 15 + 16 × 17.029 = 15 + 272.470 = 287.470

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