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Square Root of 1400

The square root of 1400 is expressed as √1400 in the radical form and as (1400)^½ or (1400)^0.5 in the exponent form. The square root of 1400 rounded up to 9 decimal places is 37.416573868. It is the positive solution of the equation x² = 1400. We can express the square root of 1400 in its lowest radical form as 10 √14.

Square Root of 1400: 37.416573867739416
Square Root of 1400 in exponential form: (1400)^½ or (1400)^0.5
Square Root of 1400 in radical form: √1400 or 10 √14

Square Root of 1400

1.	What is the Square Root of 1400?
2.	How to find the Square Root of 1400?
3.	Is the Square Root of 1400 Irrational?
4.	FAQs

What is the Square Root of 1400?

The square root of 1400, (or root 1400), is the number which when multiplied by itself gives the product as 1400. Therefore, the square root of 1400 = √1400 = 10 √14 = 37.416573867739416.

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How to Find Square Root of 1400?

Square Root of 1400 by Long Division Method

Value of √1400 by Long Division Method

Explanation:

Forming pairs: 14 and 00
Find a number Y (3) such that whose square is <= 14. Now divide 14 by 3 with quotient as 3.
Bring down the next pair 00, to the right of the remainder 5. The new dividend is now 500.
Add the last digit of the quotient (3) to the divisor (3) i.e. 3 + 3 = 6. To the right of 6, find a digit Z (which is 7) such that 6Z × Z <= 500. After finding Z, together 6 and Z (7) form a new divisor 67 for the new dividend 500.
Divide 500 by 67 with the quotient as 7, giving the remainder = 500 - 67 × 7 = 500 - 469 = 31.
Now, let's find the decimal places after the quotient 37.
Bring down 00 to the right of this remainder 31. The new dividend is now 3100.
Add the last digit of quotient to divisor i.e. 7 + 67 = 74. To the right of 74, find a digit Z (which is 4) such that 74Z × Z <= 3100. Together they form a new divisor (744) for the new dividend (3100).
Divide 3100 by 744 with the quotient as 4, giving the remainder = 3100 - 744 × 4 = 3100 - 2976 = 124.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 1400.

Therefore, the square root of 1400 by long division method is 37.4 approx.

Is Square Root of 1400 Irrational?

The actual value of √1400 is undetermined. The value of √1400 up to 25 decimal places is 37.41657386773941385583749. Hence, the square root of 1400 is an irrational number.

☛ Also Check:

Square Root of 97 - √97 = 9.84886
Square Root of 76 - √76 = 8.71780
Square Root of 324 - √324 = 18
Square Root of 36 - √36 = 6
Square Root of 325 - √325 = 18.02776
Square Root of 49 - √49 = 7
Square Root of 11 - √11 = 3.31662

Square Root of 1400 Solved Examples

Example 1: Solve the equation x² − 1400 = 0

Solution:

x² - 1400 = 0 i.e. x² = 1400
x = ±√1400
Since the value of the square root of 1400 is 37.417,
⇒ x = +√1400 or -√1400 = 37.417 or -37.417.
Example 2: If the area of a circle is 1400π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 1400π in²
⇒ r = ±√1400 in
Since radius can't be negative,
⇒ r = √1400
The square root of 1400 is 37.417.
⇒ r = 37.417 in
Example 3: If the surface area of a cube is 8400 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 = 8400 in²
⇒ a = ±√1400 in
Since length can't be negative,
⇒ a = √1400
We know that the square root of 1400 is 37.417.
⇒ a = 37.417 in

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FAQs on the Square Root of 1400

What is the Value of the Square Root of 1400?

The square root of 1400 is 37.41657.

Why is the Square Root of 1400 an Irrational Number?

Upon prime factorizing 1400 i.e. 2³ × 5² × 7¹, 2 is in odd power. Therefore, the square root of 1400 is irrational.

What is the Square Root of 1400 in Simplest Radical Form?

We need to express 1400 as the product of its prime factors i.e. 1400 = 2 × 2 × 2 × 5 × 5 × 7. Therefore, √1400 = √2 × 2 × 2 × 5 × 5 × 7 = 10 √14. Thus, the square root of 1400 in the lowest radical form is 10 √14.

Evaluate 10 plus 9 square root 1400

The given expression is 10 + 9 √1400. We know that the square root of 1400 is 37.417. Therefore, 10 + 9 √1400 = 10 + 9 × 37.417 = 10 + 336.749 = 346.749

What is the Square of the Square Root of 1400?

The square of the square root of 1400 is the number 1400 itself i.e. (√1400)² = (1400)^2/2 = 1400.

If the Square Root of 1400 is 37.417. Find the Value of the Square Root of 14.

Let us represent √14 in p/q form i.e. √(1400/100) = 14/10 = 3.742. Hence, the value of √14.0 = 3.742

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