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Square Root of 1625

The square root of 1625 is expressed as √1625 in the radical form and as (1625)^½ or (1625)^0.5 in the exponent form. The square root of 1625 rounded up to 9 decimal places is 40.311288741. It is the positive solution of the equation x² = 1625. We can express the square root of 1625 in its lowest radical form as 5 √65.

Square Root of 1625: 40.311288741492746
Square Root of 1625 in exponential form: (1625)^½ or (1625)^0.5
Square Root of 1625 in radical form: √1625 or 5 √65

Square Root of 1625

1.	What is the Square Root of 1625?
2.	How to find the Square Root of 1625?
3.	Is the Square Root of 1625 Irrational?
4.	FAQs

What is the Square Root of 1625?

The square root of 1625, (or root 1625), is the number which when multiplied by itself gives the product as 1625. Therefore, the square root of 1625 = √1625 = 5 √65 = 40.311288741492746.

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How to Find Square Root of 1625?

Square Root of 1625 by Long Division Method

Value of √1625 by Long Division Method

Explanation:

Forming pairs: 16 and 25
Find a number Y (4) such that whose square is <= 16. Now divide 16 by 4 with quotient as 4.
Bring down the next pair 25, to the right of the remainder 0. The new dividend is now 25.
Add the last digit of the quotient (4) to the divisor (4) i.e. 4 + 4 = 8. To the right of 8, find a digit Z (which is 0) such that 8Z × Z <= 25. After finding Z, together 8 and Z (0) form a new divisor 80 for the new dividend 25.
Divide 25 by 80 with the quotient as 0, giving the remainder = 25 - 80 × 0 = 25 - 0 = 25.
Now, let's find the decimal places after the quotient 40.
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. 0 + 80 = 80. To the right of 80, find a digit Z (which is 3) such that 80Z × Z <= 2500. Together they form a new divisor (803) for the new dividend (2500).
Divide 2500 by 803 with the quotient as 3, giving the remainder = 2500 - 803 × 3 = 2500 - 2409 = 91.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 1625.

Therefore, the square root of 1625 by long division method is 40.3 approximately.

Is Square Root of 1625 Irrational?

The actual value of √1625 is undetermined. The value of √1625 up to 25 decimal places is 40.31128874149274826183307. Hence, the square root of 1625 is an irrational number.

☛ Also Check:

Square Root of 240 - √240 = 15.49193
Square Root of 361 - √361 = 19
Square Root of 1521 - √1521 = 39
Square Root of 14 - √14 = 3.74166
Square Root of 50 - √50 = 7.07107
Square Root of 1681 - √1681 = 41
Square Root of 250 - √250 = 15.81139

Square Root of 1625 Solved Examples

Example 1: Solve the equation x² − 1625 = 0

Solution:

x² - 1625 = 0 i.e. x² = 1625
x = ±√1625
Since the value of the square root of 1625 is 40.311,
⇒ x = +√1625 or -√1625 = 40.311 or -40.311.
Example 2: If the area of a square is 1625 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 = 1625 in²
⇒ a = ±√1625 in
Since length can't be negative,
⇒ a = √1625 = 40.311 in
Example 3: If the surface area of a cube is 9750 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 = 9750 in²
⇒ a = ±√1625 in
Since length can't be negative,
⇒ a = √1625
We know that the square root of 1625 is 40.311.
⇒ a = 40.311 in

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FAQs on the Square Root of 1625

What is the Value of the Square Root of 1625?

The square root of 1625 is 40.31128.

Why is the Square Root of 1625 an Irrational Number?

Upon prime factorizing 1625 i.e. 5³ × 13¹, 5 is in odd power. Therefore, the square root of 1625 is irrational.

If the Square Root of 1625 is 40.311. Find the Value of the Square Root of 16.25.

Let us represent √16.25 in p/q form i.e. √(1625/100) = 16.25/10 = 4.031. Hence, the value of √16.25 = 4.031

Is the number 1625 a Perfect Square?

The prime factorization of 1625 = 5³ × 13¹. Here, the prime factor 5 is not in the pair. Therefore, 1625 is not a perfect square.

What is the Square Root of -1625?

The square root of -1625 is an imaginary number. It can be written as √-1625 = √-1 × √1625 = i √1625 = 40.311i
where i = √-1 and it is called the imaginary unit.

What is the Square of the Square Root of 1625?

The square of the square root of 1625 is the number 1625 itself i.e. (√1625)² = (1625)^2/2 = 1625.

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