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Square Root of 850

The square root of 850 is expressed as √850 in the radical form and as (850)^½ or (850)^0.5 in the exponent form. The square root of 850 rounded up to 7 decimal places is 29.1547595. It is the positive solution of the equation x² = 850. We can express the square root of 850 in its lowest radical form as 5 √34.

Square Root of 850: 29.154759474226502
Square Root of 850 in exponential form: (850)^½ or (850)^0.5
Square Root of 850 in radical form: √850 or 5 √34

Square Root of 850

1.	What is the Square Root of 850?
2.	How to find the Square Root of 850?
3.	Is the Square Root of 850 Irrational?
4.	FAQs

What is the Square Root of 850?

The square root of 850, (or root 850), is the number which when multiplied by itself gives the product as 850. Therefore, the square root of 850 = √850 = 5 √34 = 29.154759474226502.

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How to Find Square Root of 850?

Square Root of 850 by Long Division Method

Value of √850 by Long Division Method

Explanation:

Forming pairs: 08 and 50
Find a number Y (2) such that whose square is <= 8. Now divide 08 by 2 with quotient as 2.
Bring down the next pair 50, to the right of the remainder 4. The new dividend is now 450.
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 9) such that 4Z × Z <= 450. After finding Z, together 4 and Z (9) form a new divisor 49 for the new dividend 450.
Divide 450 by 49 with the quotient as 9, giving the remainder = 450 - 49 × 9 = 450 - 441 = 9.
Now, let's find the decimal places after the quotient 29.
Bring down 00 to the right of this remainder 9. The new dividend is now 900.
Add the last digit of quotient to divisor i.e. 9 + 49 = 58. To the right of 58, find a digit Z (which is 1) such that 58Z × Z <= 900. Together they form a new divisor (581) for the new dividend (900).
Divide 900 by 581 with the quotient as 1, giving the remainder = 900 - 581 × 1 = 900 - 581 = 319.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 850.

Therefore, the square root of 850 by long division method is 29.1 approx.

Is Square Root of 850 Irrational?

The actual value of √850 is undetermined. The value of √850 up to 25 decimal places is 29.15475947422650235437076. Hence, the square root of 850 is an irrational number.

☛ Also Check:

Square Root of 37 - √37 = 6.08276
Square Root of 41 - √41 = 6.40312
Square Root of 52 - √52 = 7.21110
Square Root of 169 - √169 = 13
Square Root of 50 - √50 = 7.07107
Square Root of 34 - √34 = 5.83095
Square Root of 72 - √72 = 8.48528

Square Root of 850 Solved Examples

Example 1: Solve the equation x² − 850 = 0

Solution:

x² - 850 = 0 i.e. x² = 850
x = ±√850
Since the value of the square root of 850 is 29.155,
⇒ x = +√850 or -√850 = 29.155 or -29.155.
Example 2: If the area of a circle is 850π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 850π in²
⇒ r = ±√850 in
Since radius can't be negative,
⇒ r = √850
The square root of 850 is 29.155.
⇒ r = 29.155 in
Example 3: If the area of an equilateral triangle is 850√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 = 850√3 in²
⇒ a = ±√3400 in
Since length can't be negative,
⇒ a = √3400 = 2 √850
We know that the square root of 850 is 29.155.
⇒ a = 58.310 in

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FAQs on the Square Root of 850

What is the Value of the Square Root of 850?

The square root of 850 is 29.15475.

Why is the Square Root of 850 an Irrational Number?

Upon prime factorizing 850 i.e. 2¹ × 5² × 17¹, 2 is in odd power. Therefore, the square root of 850 is irrational.

What is the Value of 1 square root 850?

The square root of 850 is 29.155. Therefore, 1 √850 = 1 × 29.155 = 29.155.

Is the number 850 a Perfect Square?

The prime factorization of 850 = 2¹ × 5² × 17¹. Here, the prime factor 2 is not in the pair. Therefore, 850 is not a perfect square.

What is the Square Root of 850 in Simplest Radical Form?

We need to express 850 as the product of its prime factors i.e. 850 = 2 × 5 × 5 × 17. Therefore, √850 = √2 × 5 × 5 × 17 = 5 √34. Thus, the square root of 850 in the lowest radical form is 5 √34.

If the Square Root of 850 is 29.155. Find the Value of the Square Root of 8.5.

Let us represent √8.5 in p/q form i.e. √(850/100) = 8.5/10 = 2.915. Hence, the value of √8.5 = 2.915

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