A day full of math games & activities. Find one near you.

Square Root of 650

The square root of 650 is expressed as √650 in the radical form and as (650)^½ or (650)^0.5 in the exponent form. The square root of 650 rounded up to 8 decimal places is 25.49509757. It is the positive solution of the equation x² = 650. We can express the square root of 650 in its lowest radical form as 5 √26.

Square Root of 650: 25.495097567963924
Square Root of 650 in exponential form: (650)^½ or (650)^0.5
Square Root of 650 in radical form: √650 or 5 √26

Square Root of 650

1.	What is the Square Root of 650?
2.	How to find the Square Root of 650?
3.	Is the Square Root of 650 Irrational?
4.	FAQs

What is the Square Root of 650?

The square root of 650, (or root 650), is the number which when multiplied by itself gives the product as 650. Therefore, the square root of 650 = √650 = 5 √26 = 25.495097567963924.

☛ Check: Square Root Calculator

How to Find Square Root of 650?

Square Root of 650 by Long Division Method

Value of √650 by Long Division Method

Explanation:

Forming pairs: 06 and 50
Find a number Y (2) such that whose square is <= 6. Now divide 06 by 2 with quotient as 2.
Bring down the next pair 50, to the right of the remainder 2. The new dividend is now 250.
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 5) such that 4Z × Z <= 250. After finding Z, together 4 and Z (5) form a new divisor 45 for the new dividend 250.
Divide 250 by 45 with the quotient as 5, giving the remainder = 250 - 45 × 5 = 250 - 225 = 25.
Now, let's find the decimal places after the quotient 25.
Bring down 00 to the right of this remainder 25. The new dividend is now 2500.
Add the last digit of quotient to divisor i.e. 5 + 45 = 50. To the right of 50, find a digit Z (which is 4) such that 50Z × Z <= 2500. Together they form a new divisor (504) for the new dividend (2500).
Divide 2500 by 504 with the quotient as 4, giving the remainder = 2500 - 504 × 4 = 2500 - 2016 = 484.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 650.

Therefore, the square root of 650 by long division method is 25.4 approximately.

Is Square Root of 650 Irrational?

The actual value of √650 is undetermined. The value of √650 up to 25 decimal places is 25.49509756796392415014112. Hence, the square root of 650 is an irrational number.

☛ Also Check:

Square Root of 33 - √33 = 5.74456
Square Root of 400 - √400 = 20
Square Root of 1521 - √1521 = 39
Square Root of 60 - √60 = 7.74597
Square Root of 61 - √61 = 7.81025
Square Root of 44 - √44 = 6.63325
Square Root of 21 - √21 = 4.58258

Square Root of 650 Solved Examples

Example 1: Solve the equation x² − 650 = 0

Solution:

x² - 650 = 0 i.e. x² = 650
x = ±√650
Since the value of the square root of 650 is 25.495,
⇒ x = +√650 or -√650 = 25.495 or -25.495.
Example 2: If the surface area of a cube is 3900 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 = 3900 in²
⇒ a = ±√650 in
Since length can't be negative,
⇒ a = √650
We know that the square root of 650 is 25.495.
⇒ a = 25.495 in
Example 3: If the area of a square is 650 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 = 650 in²
⇒ a = ±√650 in
Since length can't be negative,
⇒ a = √650 = 25.495 in

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on the Square Root of 650

What is the Value of the Square Root of 650?

The square root of 650 is 25.49509.

Why is the Square Root of 650 an Irrational Number?

Upon prime factorizing 650 i.e. 2¹ × 5² × 13¹, 2 is in odd power. Therefore, the square root of 650 is irrational.

What is the Value of 19 square root 650?

The square root of 650 is 25.495. Therefore, 19 √650 = 19 × 25.495 = 484.407.

Is the number 650 a Perfect Square?

The prime factorization of 650 = 2¹ × 5² × 13¹. Here, the prime factor 2 is not in the pair. Therefore, 650 is not a perfect square.

What is the Square Root of 650 in Simplest Radical Form?

We need to express 650 as the product of its prime factors i.e. 650 = 2 × 5 × 5 × 13. Therefore, √650 = √2 × 5 × 5 × 13 = 5 √26. Thus, the square root of 650 in the lowest radical form is 5 √26.

Evaluate 9 plus 10 square root 650

The given expression is 9 + 10 √650. We know that the square root of 650 is 25.495. Therefore, 9 + 10 √650 = 9 + 10 × 25.495 = 9 + 254.951 = 263.951

Math worksheets and
visual curriculum