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Square Root of 750

The square root of 750 is expressed as √750 in the radical form and as (750)^½ or (750)^0.5 in the exponent form. The square root of 750 rounded up to 10 decimal places is 27.3861278753. It is the positive solution of the equation x² = 750. We can express the square root of 750 in its lowest radical form as 5 √30.

Square Root of 750: 27.386127875258307
Square Root of 750 in exponential form: (750)^½ or (750)^0.5
Square Root of 750 in radical form: √750 or 5 √30

Square Root of 750

1.	What is the Square Root of 750?
2.	How to find the Square Root of 750?
3.	Is the Square Root of 750 Irrational?
4.	FAQs

What is the Square Root of 750?

The square root of 750, (or root 750), is the number which when multiplied by itself gives the product as 750. Therefore, the square root of 750 = √750 = 5 √30 = 27.386127875258307.

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How to Find Square Root of 750?

Square Root of 750 by Long Division Method

Value of √750 by Long Division Method

Explanation:

Forming pairs: 07 and 50
Find a number Y (2) such that whose square is <= 7. Now divide 07 by 2 with quotient as 2.
Bring down the next pair 50, to the right of the remainder 3. The new dividend is now 350.
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 7) such that 4Z × Z <= 350. After finding Z, together 4 and Z (7) form a new divisor 47 for the new dividend 350.
Divide 350 by 47 with the quotient as 7, giving the remainder = 350 - 47 × 7 = 350 - 329 = 21.
Now, let's find the decimal places after the quotient 27.
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. 7 + 47 = 54. To the right of 54, find a digit Z (which is 3) such that 54Z × Z <= 2100. Together they form a new divisor (543) for the new dividend (2100).
Divide 2100 by 543 with the quotient as 3, giving the remainder = 2100 - 543 × 3 = 2100 - 1629 = 471.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 750.

Therefore, the square root of 750 by long division method is 27.3 approximately.

Is Square Root of 750 Irrational?

The actual value of √750 is undetermined. The value of √750 up to 25 decimal places is 27.38612787525830567284849. Hence, the square root of 750 is an irrational number.

☛ Also Check:

Square Root of 900 - √900 = 30
Square Root of 37 - √37 = 6.08276
Square Root of 40 - √40 = 6.32456
Square Root of 196 - √196 = 14
Square Root of 120 - √120 = 10.95445
Square Root of 15 - √15 = 3.87298
Square Root of 109 - √109 = 10.44031

Square Root of 750 Solved Examples

Example 1: Solve the equation x² − 750 = 0

Solution:

x² - 750 = 0 i.e. x² = 750
x = ±√750
Since the value of the square root of 750 is 27.386,
⇒ x = +√750 or -√750 = 27.386 or -27.386.
Example 2: If the surface area of a cube is 4500 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 = 4500 in²
⇒ a = ±√750 in
Since length can't be negative,
⇒ a = √750
We know that the square root of 750 is 27.386.
⇒ a = 27.386 in
Example 3: If the area of a square is 750 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 = 750 in²
⇒ a = ±√750 in
Since length can't be negative,
⇒ a = √750 = 27.386 in

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FAQs on the Square Root of 750

What is the Value of the Square Root of 750?

The square root of 750 is 27.38612.

Why is the Square Root of 750 an Irrational Number?

Upon prime factorizing 750 i.e. 2¹ × 3¹ × 5³, 2 is in odd power. Therefore, the square root of 750 is irrational.

If the Square Root of 750 is 27.386. Find the Value of the Square Root of 7.5.

Let us represent √7.5 in p/q form i.e. √(750/100) = 7.5/10 = 2.739. Hence, the value of √7.5 = 2.739

What is the Value of 13 square root 750?

The square root of 750 is 27.386. Therefore, 13 √750 = 13 × 27.386 = 356.020.

Is the number 750 a Perfect Square?

The prime factorization of 750 = 2¹ × 3¹ × 5³. Here, the prime factor 2 is not in the pair. Therefore, 750 is not a perfect square.

What is the Square of the Square Root of 750?

The square of the square root of 750 is the number 750 itself i.e. (√750)² = (750)^2/2 = 750.

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